Question

The surface area of a sphere is 32π cm${}^2$. Find the radius and volume of this sphere?

• A. $2\sqrt{2}cm,\frac{64\pi }{3}c{m}^3$
• B. $8cm,\frac{64\pi }{3}c{m}^3$
• C. $16cm,\frac{64\pi }{3}c{m}^3$
• D. $2\sqrt{2}cm,\frac{64\sqrt{2}\pi }{3}c{m}^3$

Answer 1

The correct option is D $2\sqrt{2}cm,\frac{64\sqrt{2}\pi }{3}c{m}^3$

Given: Surface area of the sphere, S = $32\pi c{m}^2$
We know, surface area of a sphere of radius r is $4\pi r^2.$
$\Rightarrow 4\pi r^2=32\pi \Rightarrow r^2=\frac{32\pi }{4\pi }\Rightarrow r^2=8\Rightarrow r=2\sqrt{2}cm\text{Now, volume of sphere}=\frac{4}{3}\pi r^3=\frac{4\pi (2\sqrt{2}{)}^3}{3}=\frac{64\sqrt{2}\pi }{3}c{m}^3$