Question

To the nearest whole number, what is the surface area of a sphere with a volume of 140 cm3?

Answer 1

Answer: $130\ cm^2$

Step-by-step explanation:

The volume of sphere is given by :-

$V=\dfrac{4}{3}\pi r^3$, where r is radius of sphere.

Given : The volume of sphere = $140\ cm^3$

$\Rightarrow\ 140=\dfrac{4}{3} (3.14) r^3\\\\\Rightarrow\ r^3=\dfrac{140\times3}{4\times (3.14)}\\\\\Rightarrow\ r^3=33.4394904459\approx33.44$

Taking cube root on both sides , we get

$r=\sqrt[3]{33.44}=3.22171078046\approx3.22\ cm$

The surface area of sphere is given by :-

$S.A=4\pi r^2\\\\\Rightarrow\ S.A.=4(3.14)(3.22)^2\\\\\Rightarrow\ S.A.=130.227104\approx130\ cm^2$

Answer 2

We know that V= 4/3 pi r^3

So r^3= 140/ ((4/3) pi)= 33.422538

Hence r= 3.221166

SA = 4 pi r^2
= 4 pi 3.221166^2
= 130.39 cm^2
= 130 cm^2