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Surface Area And Volume of Sphere — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSSurface Area And Volume of Sphere1 Mark
Question
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
  1. $4\pi\text{r}^3$
  2. $\frac{8}{3}\pi\text{r}^3$
  3. $2\pi\text{r}^3$
  4. $8\pi\text{r}^3$
✓

Answer

  1. $2\pi\text{r}^3$
Solution:

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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