Question

A volume of a coin is 113.04 mm2 what is the approximate of a sphere that has the same height and a circular base with the same diameter?Use 3.14 for x round to the nearest hundredth

Answer 1

We have been given that the volume of a cone is 113.04 cubic mm. We are asked to find the approximate volume of a sphere that has the same height and a circular base with the same diameter.

We know that volume of cone is $\frac{1}{3}\pi r^2\cdot h$.

The height is equal to the diameter. We know that diameter is 2 times radius, so we can represent this information in an equation as:

$h=2r$

Upon substituting $h=2r$ in volume of cone, we will get:

$V=\frac{1}{3}\pi r^2\cdot 2r$

$V=\frac{2}{3}\pi r^3$

We know that volume of sphere is $V=\frac{4}{3}\pi r^3$.

Upon comparing volume of cone with volume of sphere, we can see that volume of sphere is 2 times the volume of cone.

$V=2(\frac{2}{3}\pi r^3)$

Since $\frac{2}{3}\pi r^3=113.04$, so volume of sphere would be:

$V=2(113.04)$

$V=226.08$

Therefore, volume of sphere would be 226.08 cubic mm.