The surface area of a sphere is 616m2. what is the volume of-the sphere (correct to two significant figures)? (take \pi = 3.142)
A
14 cm\(^3\)
B
210 cm\(^3\)
C
1,400 cm\(^3\)
D
2,100 cm\(^3\)
E
4,300 cm\(^3\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(Surface area (A) = 4\pi r^{2} = 616m^{2}\)
solving, we have
\(r = 7m\)
\(Volume = \frac{4}{3}\pi r^{3}\)
\(Volume = \frac{4\times 3.142 \times 7^{3}}{3}\)
\(Volume = \frac{4310.824}{3}\)
= \(1436.941m^{3} \approxeq 1400m^{3}(2 sig. fig)\)
Source: Myschool Past Questions Archive (Record #41880)