Question

Find the radius of a sphere that has a volume of 2 liters.

Answer 1

ANSWER

7.82 cm

EXPLANATION

We want to find the radius of a sphere that has a volume of 2 liters.

First, let us convert the volume of the sphere to cubic centimetres.

We have that:

1 litre = 1000 cubic centimetres:

=> 2 litres = 2 * 1000 = 2000 cubic centimetres

The volume of a sphere is given as:

$V=\frac{4}{3}\pi\cdot r^3$

where r = radius

Therefore, we have that, for the given sphere:

$\begin{gathered} 2000=\frac{4}{3}\cdot\pi\cdot r^3 \\ \text{Multiply both sides by }\frac{3}{4\pi}\colon \\ 2000\cdot\frac{3}{4\pi}=r^3 \\ r^3=477.46 \\ \text{ Find the cube root of both sides:} \\ r=\sqrt[3]{477.46} \\ r=7.82\operatorname{cm} \end{gathered}$

That is the radius of the sphere.