The surface area of a sphere is $\frac{792}{7} cm^2$. Find, correct to the nearest whole number, its volume. [Take $\pi = \frac{22}{7}$]

Step 1: Analyze the question We're given the surface area of a sphere and need to find its volume. First we find the radius from the surface area, then use it in the volume formula.

Step 2: Concepts and formulas

• Surface area of a sphere: A = 4πr²
• Volume of a sphere: V = (4/3)πr³

Step 3: Solve

Find r:

4 × (22/7) × r² = 792/7

(88/7) r² = 792/7

r² = 792/88 = 9

r = 3 cm

Find the volume:

V = (4/3) × (22/7) × 3³ V = (4/3) × (22/7) × 27 V = 4 × 22 × 9 / 7 V = 792/7 V ≈ 113.14 cm³

To the nearest whole number, V ≈ 113 cm³.

Step 4: Answer The volume is 113 cm³, which is option A.

Tip: Notice that with r = 3, the volume 792/7 equals the surface area given. That is a coincidence because V = (r/3) × A, and r/3 = 1 here. In general, V = (A × r)/3, which is a quick shortcut: once you have r, multiply by the surface area and divide by 3. Also, when you see a number like 792/7, check whether dividing by 88 gives a perfect square, as it does here (9).