A sphere is placed inside a right circular cylinder so as to touc… - Vidyadip

MCQ

A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is $r,$ then the volume of the cylinder is

A
$4\pi\text{r}^3$
B
$\frac{8}{3}\pi\text{r}^3$
✓
$2\pi\text{r}^3$
D
$8\pi\text{r}^3$

✓

Answer

Correct option: C.

$2\pi\text{r}^3$

Radius of sphere $= r$
Sphere touches cylinder at Top, Base and Lateral Surface.
Then,
$2r =$ height of cylinder $= h$
$r =$ Radius of cylinder
Volume of cylinder $=\pi\text{r}^2\text{h}$
$=\pi\text{r}^2(2\text{r})$
$=2\pi\text{r}^3$
Hence, correct option is $(c).$

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