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Surface Areas and Volumes — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Areas and Volumes1 Mark
Question
Write True or False and justify your answer in the following: A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.
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Answer

Let $r$ the radius and $h$ be hight of the cylinder and a right circular cone.
Now, volume of cylinder $=\pi\text{r}^2\text{h}$
And volume of cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$\pi\text{r}^2\text{h}=\frac{1}{3}\pi\text{r}^2\text{h}$
$\Rightarrow3\pi\text{r}^2\text{h}=\pi\text{r}^2\text{h}$
Therefore, volume of cylinder $= 3($volume of cone$)$
Hence, the given statement is true.

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