Sphere Surface Area Math Example 2

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Example 2

medium
A sphere has a surface area of 100π100\pi cm². Find its radius and volume.

Solution

  1. 1
    Step 1: Set up the equation: 4πr2=100π4\pi r^2 = 100\pi.
  2. 2
    Step 2: Divide both sides by 4π4\pi: r2=25r^2 = 25, so r=5r = 5 cm.
  3. 3
    Step 3: Find the volume using V=43πr3=43π(5)3=43π(125)=500π3V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi(5)^3 = \frac{4}{3}\pi(125) = \frac{500\pi}{3}.
  4. 4
    Step 4: V≈523.6V \approx 523.6 cm³.

Answer

r=5r = 5 cm; V=500π3≈523.6V = \frac{500\pi}{3} \approx 523.6 cm³
Working backwards from surface area to radius: divide SA by 4π4\pi and take the square root. Once r = 5 is known, the volume formula 43πr3\frac{4}{3}\pi r^3 gives 500π3\frac{500\pi}{3} cm³.

About Sphere Surface Area

The total area covering the curved outer surface of a sphere, given by the formula S=4πr2S = 4\pi r^2.

Learn more about Sphere Surface Area →

More Sphere Surface Area Examples

Example 1 easy

Find the surface area of a sphere with radius [formula] cm.

Example 3 medium

Find the surface area of a sphere with diameter 10 cm.

Example 4 easy

A basketball has a diameter of [formula] cm. Find its surface area.

Example 5 hard

Two spheres have radii in the ratio [formula]. Find the ratio of their surface areas. If the smaller

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