The surface area of a sphere is calculated using the formula 4 * π * r^2, where “r” is the radius of the sphere. It represents the total area of the curved surface of the sphere. The surface area is measured in square units, such as square centimeters (cm^2) or square meters (m^2).
Sphere Surface Area Calculator
| Radius (r) | Surface Area (4 * π * r^2) |
|---|---|
| 1 cm | 4 * π * (1 cm)^2 ≈ 12.57 cm^2 |
| 2 cm | 4 * π * (2 cm)^2 ≈ 50.27 cm^2 |
| 3 cm | 4 * π * (3 cm)^2 ≈ 113.10 cm^2 |
| 4 cm | 4 * π * (4 cm)^2 ≈ 201.06 cm^2 |
| 5 cm | 4 * π * (5 cm)^2 ≈ 314.16 cm^2 |
| 6 cm | 4 * π * (6 cm)^2 ≈ 452.39 cm^2 |
| 7 cm | 4 * π * (7 cm)^2 ≈ 615.75 cm^2 |
| 8 cm | 4 * π * (8 cm)^2 ≈ 804.25 cm^2 |
| 9 cm | 4 * π * (9 cm)^2 ≈ 1017.88 cm^2 |
| 10 cm | 4 * π * (10 cm)^2 ≈ 1256.64 cm^2 |
FAQs
How do you find the surface area of a sphere?
The surface area of a sphere can be calculated using the formula: Surface Area = 4 * π * r^2, where "r" is the radius of the sphere.
What is the surface area of a 12 cm sphere?
The surface area of a sphere with a radius of 12 cm can be calculated as follows: Surface Area = 4 * π * (12 cm)^2 = 4 * π * 144 cm^2 ≈ 1809.56 cm^2
Why is the surface area of a sphere 4πr^2?
The formula for the surface area of a sphere, 4πr^2, is derived from integrating the surface area element of a sphere. It represents the sum of all the infinitesimal areas of the sphere's curved surface.
How do you calculate surface area?
Surface area can be calculated differently for different shapes. For example, for a cube, you add up the areas of all six faces. For a sphere, you use the formula 4πr^2.
What is a formula for a sphere?
The formula for the surface area of a sphere is 4 * π * r^2, and the formula for the volume of a sphere is (4/3) * π * r^3, where "r" is the radius of the sphere.
What is the formula for surface area and volume of a sphere?
The formula for the surface area of a sphere is 4 * π * r^2, and the formula for the volume of a sphere is (4/3) * π * r^3, where "r" is the radius of the sphere.
What is the surface area of a 4cm sphere?
The surface area of a sphere with a radius of 4 cm can be calculated as follows: Surface Area = 4 * π * (4 cm)^2 = 4 * π * 16 cm^2 ≈ 201.06 cm^2
What is the 21 cm surface area of a sphere of diameter?
The question seems incomplete. To find the surface area of a sphere with a diameter of 21 cm, we need to use the radius, which is half of the diameter. The surface area can be calculated using the formula 4 * π * r^2, where "r" is the radius.
What is the surface area of a sphere of radius 14 cm?
The surface area of a sphere with a radius of 14 cm can be calculated as follows: Surface Area = 4 * π * (14 cm)^2 = 4 * π * 196 cm^2 ≈ 2463.08 cm^2
What is 4 * π * r^2 for a sphere?
4 * π * r^2 represents the surface area of a sphere with a radius "r." It is the sum of all the areas of the sphere's curved surface.
Why is surface area always squared?
Surface area is always squared because it represents the area of a two-dimensional surface. When we calculate the surface area of an object, we are adding up the areas of all its individual flat surfaces.
What is the easiest way to calculate surface area?
The easiest way to calculate the surface area of an object depends on the object's shape. For simple shapes like cubes and spheres, there are well-known formulas. For irregular shapes, you can use approximations or more advanced mathematical methods.
How do you manually calculate surface area?
To manually calculate the surface area of an object, you need to find the area of each face or surface of the object and then add them together.
How do you find the surface area for beginners?
For beginners, finding the surface area involves calculating the area of each side or face of the object and then adding them together.
What is a sphere for kids?
A sphere is a three-dimensional geometric shape that looks like a ball. It is perfectly round and has the same distance from its center to any point on its surface.
Why is the volume of a sphere 4/3?
The volume of a sphere is 4/3 times π times the radius cubed (4/3 * π * r^3) because it is a result of the integration process when finding the volume of a sphere.
How do you find surface area and volume?
The surface area of an object is the sum of the areas of all its individual surfaces, and the volume is the amount of space the object occupies. To find these, you need to know the appropriate formulas for the specific shape of the object.
What is the formula for surface area to volume?
The formula for surface area to volume ratio depends on the shape of the object. For a sphere, the ratio is 3/r, where "r" is the radius.
How do you find the surface area of a sphere with the circumference?
You cannot find the surface area of a sphere with just the circumference. To calculate the surface area, you need either the radius or the diameter of the sphere.
What is the surface area of the sphere if its radius is 7cm?
The surface area of a sphere with a radius of 7 cm can be calculated as follows: Surface Area = 4 * π * (7 cm)^2 = 4 * π * 49 cm^2 ≈ 615.75 cm^2
Is 40 cm 4 find the surface area of a sphere of radius 7 cm?
The question seems incomplete. To find the surface area of a sphere with a radius of 7 cm, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is the surface area of a sphere of radius 5.6 cm 4?
The question seems incomplete. To find the surface area of a sphere with a radius of 5.6 cm, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is the surface area of a sphere having 5cm?
The question seems incomplete. To find the surface area of a sphere with a radius of 5 cm, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is the surface area of a sphere of radius 10.5 cm?
The surface area of a sphere with a radius of 10.5 cm can be calculated as follows: Surface Area = 4 * π * (10.5 cm)^2 = 4 * π * 110.25 cm^2 ≈ 1385.44 cm^2
What is the volume of a sphere of diameter 42 cm?
To find the volume of a sphere with a diameter of 42 cm, first, we need to find the radius, which is half of the diameter. The volume can then be calculated using the formula (4/3) * π * r^3.
What is the surface area of 154 cm2 sphere?
The question seems incomplete. To find the surface area of a sphere with an area of 154 cm^2, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is the surface area of a sphere of radius 40 cm?
The surface area of a sphere with a radius of 40 cm can be calculated as follows: Surface Area = 4 * π * (40 cm)^2 = 4 * π * 1600 cm^2 ≈ 20106.17 cm^2
What is the surface area of a sphere is 154 cm square?
The question seems incomplete. To find the surface area of a sphere with an area of 154 cm^2, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is "R" in a sphere?
In a sphere, "R" usually represents the radius of the sphere, which is the distance from the center of the sphere to any point on its surface.
What is the volume of a sphere if "R" is 2?
If "R" represents the radius of a sphere and its value is 2, the volume can be calculated using the formula (4/3) * π * (2^3) = (4/3) * π * 8 = 32/3 * π ≈ 33.51 cubic units.
What does 2πr equal?
2πr represents the circumference of a circle with a radius "r."
What is the 4 * π * r^2 formula for?
The formula 4 * π * r^2 represents the surface area of a sphere with a radius "r." It is the sum of all the areas of the sphere's curved surface.
What formula is π * d^2 / 4?
The formula π * d^2 / 4 represents the area of a circle when given the diameter "d." It is derived from the formula for the area of a circle, which is π * r^2, by replacing the radius "r" with half of the diameter "d."
What is π/4 times diameter?
π/4 times the diameter represents the area of a circle when given the diameter "d." It is derived from the formula for the area of a circle, which is π * r^2, by replacing the radius "r" with half of the diameter "d."
How do you explain area to a child?
Area is the amount of space a flat surface takes up. It is measured in square units, such as square centimeters or square meters. For example, the area of a rectangle is found by multiplying its length and width.
Is the surface area of a sphere squared or cubed?
The surface area of a sphere is squared because it represents the area of a two-dimensional curved surface. It is not cubed, which would be related to the volume.
Should surface area be squared?
Yes, surface area should be squared because it represents the area of a two-dimensional surface, and when we calculate the surface area of an object, we are adding up the areas of all its individual flat surfaces.
How do I get the volume of a sphere?
To get the volume of a sphere, you can use the formula (4/3) * π * r^3, where "r" is the radius of the sphere.
What is the surface area in GCSE maths?
In GCSE maths, surface area refers to the total area of all the surfaces of a three-dimensional object. It is calculated by finding the areas of all the individual faces or surfaces and adding them together.
What is the difference between surface area and total surface area?
Surface area and total surface area both refer to the sum of the areas of all the faces or surfaces of a three-dimensional object. However, "surface area" is a general term, while "total surface area" usually refers to the area of all the external surfaces of the object.
How do you find the surface area of an irregular shape?
To find the surface area of an irregular shape, you can use various methods, such as dividing the shape into smaller regular shapes whose areas you can calculate and then adding them together, or using advanced mathematical techniques like calculus.
How do you solve surface area questions?
To solve surface area questions, you need to identify the shape of the object and use the appropriate formula for calculating its surface area. For more complex objects, you might need to break them down into simpler shapes and then add up their individual surface areas.
How do you find the area of an irregular-shaped object?
To find the area of an irregular-shaped object, you can use the method of approximation, where you divide the shape into smaller regular shapes whose areas you can calculate and then add them together. Another option is to use advanced mathematical techniques like calculus.
How do you explain surface area to students?
Surface area is the total area of all the surfaces of a three-dimensional object. It is like wrapping the object with paper, and surface area measures the amount of paper needed to cover all its sides.
Is sphere and circle the same?
No, a sphere and a circle are not the same. A circle is a two-dimensional shape with all points equidistant from its center lying on the same plane, while a sphere is a three-dimensional shape with all points equidistant from its center, forming a perfectly round ball.
Is a sphere a circle?
A sphere is not a circle, but a circle is a two-dimensional representation of a sphere. A sphere is a three-dimensional shape, while a circle is a flat, two-dimensional shape.
Is a balloon a sphere?
A balloon can be shaped like a sphere when fully inflated. However, when it is not inflated or partially inflated, it may not perfectly resemble a sphere.
How do you find the area of a circle?
To find the area of a circle, you use the formula: Area = π * r^2, where "r" is the radius of the circle.
Why is the area of a sphere 4 times a circle?
The surface area of a sphere is four times the area of a circle with the same radius because a sphere is like a stack of infinite circles from the bottom to the top, and each circle's area adds up to the total surface area.
How to find radius?
To find the radius of a circle, you need either the diameter or the circumference. If you have the diameter, divide it by 2 to get the radius. If you have the circumference, divide it by 2π to get the radius.
Is the diameter half the radius?
No, the diameter is not half the radius. The diameter of a circle is equal to twice the radius, so you can find the radius by dividing the diameter by 2.
How to calculate area?
To calculate the area of a two-dimensional shape, you multiply the length and width for rectangles, use the formula π * r^2 for circles, and use the appropriate formula for other shapes.
Why is the area of a square "a^2"?
The area of a square is "a^2" because it represents the number of unit squares that can fit inside the square. Each side of the square is "a" units long, so the total area is "a * a" or "a^2."
What are all the surface area formulas?
The surface area formulas depend on the shape of the object. Some common formulas include:
- Cube: Surface Area = 6 * side^2
- Rectangular Prism: Surface Area = 2 * (length * width + length * height + width * height)
- Sphere: Surface Area = 4 * π * r^2
- Cylinder: Surface Area = 2 * π * r * (r + height)
- Cone: Surface Area = π * r * (r + √(r^2 + height^2))
What is the relationship between volume and surface area of a sphere?
The relationship between volume and surface area of a sphere is that as the volume increases, the surface area also increases, but not at the same rate. The volume increases as the cube of the radius, while the surface area increases only as the square of the radius.
Is surface area and volume the same thing?
No, surface area and volume are not the same thing. Surface area refers to the total area of all the surfaces of a three-dimensional object, while volume refers to the amount of space the object occupies.
What is the surface area of a 4cm sphere?
The surface area of a sphere with a radius of 4 cm can be calculated as follows: Surface Area = 4 * π * (4 cm)^2 = 4 * π * 16 cm^2 ≈ 201.06 cm^2
How to find the surface area and volume of a sphere calculator?
To find the surface area and volume of a sphere, you can use the appropriate formulas and plug in the values of the radius or diameter into the calculator.
What is the total surface area of a hemisphere of radius 21 cm?
A hemisphere is half of a sphere, so its total surface area is half of the surface area of a full sphere with the same radius. The surface area of a hemisphere with a radius of 21 cm can be calculated as follows: Surface Area = 2 * (4 * π * (21 cm)^2) = 2 * (4 * π * 441 cm^2) = 3528 cm^2
What was the surface area of one ball of 7 mm radius?
The surface area of one ball with a radius of 7 mm can be calculated as follows: Surface Area = 4 * π * (7 mm)^2 = 4 * π * 49 mm^2 ≈ 615.75 mm^2
What is the surface area of a sphere of diameter 14 cm?
To find the surface area of a sphere with a diameter of 14 cm, first, we need to find the radius, which is half of the diameter. The surface area can then be calculated using the formula 4 * π * r^2.
What is the total surface area of a sphere whose radius is 1.4 cm 4?
The question seems incomplete. To find the total surface area of a sphere with a radius of 1.4 cm, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is the radius of a sphere if its surface area is 448.5 cm square?
To find the radius of a sphere with a given surface area of 448.5 cm^2, you can use the formula for surface area: 4 * π * r^2. Rearrange the formula to solve for "r" and then plug in the surface area value.
What is the volume of a sphere of diameter 42 cm?
To find the volume of a sphere with a diameter of 42 cm, first, we need to find the radius, which is half of the diameter. The volume can then be calculated using the formula (4/3) * π * r^3.
What is the surface area of 154 cm2 sphere?
The question seems incomplete. To find the surface area of a sphere with an area of 154 cm^2, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is the surface area of a sphere of radius 40 cm?
The surface area of a sphere with a radius of 40 cm can be calculated as follows: Surface Area = 4 * π * (40 cm)^2 = 4 * π * 1600 cm^2 ≈ 20106.17 cm^2
What is the surface area of a sphere is 154 cm square?
The question seems incomplete. To find the surface area of a sphere with an area of 154 cm^2, you need to use the formula 4 * π * r^2, where "r" is the radius.
What is R in a sphere?
In a sphere, "R" usually represents the radius of the sphere, which is the distance from the center of the sphere to any point on its surface.
What is the volume of a sphere if R is 2?
If "R" represents the radius of a sphere and its value is 2, the volume can be calculated using the formula (4/3) * π * (2^3) = (4/3) * π * 8 = 32/3 * π ≈ 33.51 cubic units.
What does 2πr equal?
2πr represents the circumference of a circle with a radius "r."
What is the 4 * π * r^2 formula for?
The formula 4 * π * r^2 represents the surface area of a sphere with a radius "r." It is the sum of all the areas of the sphere's curved surface.
What formula is π * d^2 / 4?
The formula π * d^2 / 4 represents the area of a circle when given the diameter "d." It is derived from the formula for the area of a circle, which is π * r^2, by replacing the radius "r" with half of the diameter "d."
What is π/4 times diameter?
π/4 times the diameter represents the area of a circle when given the diameter "d." It is derived from the formula for the area of a circle, which is π * r^2, by replacing the radius "r" with half of the diameter "d."
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