Question

If the sphere has a surface area of 256π cm${}^2$, what is its volume (approximated value)?

• A. $483\pi c{m}^3$
• B. $583\pi c{m}^3$
• C. $683\pi c{m}^3$
• D. $883\pi c{m}^3$

Answer 1

The correct option is C $683\pi c{m}^3$

Given, surface area of the sphere = 256π

We know that the surface area of a sphere = $4\pi r^2$
So, $4\pi r^2=256\pi$
$\Rightarrow r^2=\frac{256}{4}$
$\Rightarrow r^2=64$
$\Rightarrow r=\sqrt{64}=8cm$
Therefore, radius of the sphere = 8 cm

Now, volume of the sphere is
= $\frac{4}{3}\pi r^3$
= $\frac{4}{3}\times \pi \times (8{)}^3$
= $\frac{4\times 512}{3}\pi$
= $\frac{2048}{3}\pi$
= $682.66\pi c{m}^3$
$\approx 683\pi c{m}^3$