Question
A cylinder whose height is two thirds of its diameter has the same volume as a sphere of radius 4cm. Calculate the radius of the base of the cylinder.
✓
Answer
Given that Height of the cylinder $=\frac{2}{3\text{ diameter}}$ We know that Diameter = 2(radius)$\text{h}=\frac{2}{3}\times2\text{r}=\frac{4}{3\text{r}}$
Volume of the cylinder = Volume of the sphere$\pi\text{r}^2\text{h}=\frac{4}{3\pi\text{r}^3}$
$\pi\times\text{r}^2\times(\frac{4}{3\text{r}})=\frac{4}{3\pi(4)^3}$
$(\text{r})^3=(\text{4)}^3$
$\text{r}=4\text{cm}$
Volume of the cylinder = Volume of the sphere$\pi\text{r}^2\text{h}=\frac{4}{3\pi\text{r}^3}$
$\pi\times\text{r}^2\times(\frac{4}{3\text{r}})=\frac{4}{3\pi(4)^3}$
$(\text{r})^3=(\text{4)}^3$
$\text{r}=4\text{cm}$
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