Q&A for How to Find the Radius of a Sphere

Write an equation whereby the volume [(4πr³) / 3] is set equal to three times the surface area (4πr²). Thus, [(4πr³) / 3] = 12πr². Divide both sides by 4π, so that r³/3 = r². Multiply by 3: r³ = 3r². Divide by r²: r = 3. In other words, a sphere's volume can be three times its surface area only if its radius is 3 units.

You can get a very close approximation by carefully measuring the circumference and dividing by twice-pi (6.28).

The surface area (S) of a sphere equals 4πr², where r is the radius. Using that equation to solve for r: r = √(S / 4π). Now substitute 20 for S, and solve for the radius of sphere A: r = √(20 / 4π) = √(20 / 12.56) = √ 1.59 = 1.26 cm. That's the radius of sphere A. The radius of sphere B is three times the radius of sphere A: (3)(1.26) = 3.79 cm. So for sphere B, the surface area is 4πr² = (4)(3.14)(3.79)² = 180.4 square centimeters. (That answer makes sense, because when you multiply the radius of a sphere by 3, you multiply its surface area by 3² or 9.) (We didn't exactly triple the original surface area, because we rounded off some numbers along the way.)

Use the formula A = 2πr², which would be half the surface area of the full sphere.

You would have to know other information. If, for example, you know the surface area (A) of the hemisphere, divide it by 2π, then find the square root of that number. Thus, r = √(A / 2π).

Mark any other point on the surface of the sphere.Find the distance between them and that's it, you get the radius.

Yes, a circle's diameter is equal to its circumference divided by pi. (The commutative law is irrelevant.)

Assuming a solid aluminum sphere, you would first need to know the density of aluminum. Then find the volume (4/3)(πr³). Then multiply the volume by the density.

The cross-sectional area (31 sq in) equals πr². So r² = 31 / π = 9.87. Therefore, r = 3.14 inches. The surface area of a sphere equals 4πr², so the surface area of this sphere is (4)(π)(3.14)² = 123.84 sq in.

A sphere does not have length, breadth or height. It has a diameter, which (if not given to you) may be measured with a tool called a caliper.

First solve for the radius: r =½√(A/π), where A is the surface area. Then solve for the circumference: C = 2πr.

Follow the instructions in Method 1 Step 4 above.

Find its radius and double it. See Method 1 Step 3 above.

Use the volume formula (4πr³/3), then divide by 2.

Double the surface area. That gives you the surface area of the full sphere. Divide that area by 4π or 12.566. Then find the square root of that number. That's the radius of both the sphere and the hemisphere.

The volume is 4/3(πr³) = 4/3(3.14)(23)³ = 50,939.173 cubic centimeters.

Assuming by "height" you mean "diameter," the surface area formula is A = 4πr², where r is half the diameter, and π is 3.14159.

You would use the volume formula rather than the circumference formula. V = πr²h = π(0.75)²(3) = 5.3 cubic meters.

Using the radius formula in Method 1 Step 3 above, r = [(V/π)(¾)]^(1/3) = (3V / 4π) ^(1/3) = (108π / 4π)^(1/3) = 27^(1/3) = 3 cm.

In the formula, change "r³" to "(d/2)³" or "d³/8". (Alternatively, you could divide the given diameter by 2 and then use that number as the radius in the volume formula.)