The surface area of a sphere is 616m2. what is the volume of-the sphere (correct to two significant figures)? (take π = 3.142)

Analyze the question: We are given the surface area of a sphere (616) and asked for its volume to 2 significant figures, using π = 3.142.

Concept:

• Surface area = 4πr²
• Volume = (4/3)πr³

Solution:

Step 1: Find r. 4πr² = 616 r² = 616 / (4 × 3.142) = 616 / 12.568 = 49.014... r ≈ 7.001

So r ≈ 7 (the question was clearly designed with π = 22/7, giving r = 7 exactly).

Step 2: Find the volume. V = (4/3) × π × r³ r³ ≈ 343.2 (using r ≈ 7.001) V = (4/3) × 3.142 × 343.2 V ≈ 4.1893 × 343.2 ≈ 1437.8

Using r = 7 exactly gives V = 4.1893 × 343 ≈ 1437.0

To 2 significant figures: 1,400

Note on units: The question states the area in m² but the options are in cm³. This is a typo in the question. The numerical value is what matters, and the answer matches option C.

Answer: C. 1,400 (cm³)

Tip: When the surface area is a multiple of 22/7 values (like 616 = 4 × 22/7 × 49), expect a neat radius like 7. Check by working out 616 ÷ 88 = 7 (since 4 × 22/7 = 88/7, so r² = 616 × 7 / 88 = 49). Also, always check the units in the question and options, since typos happen.