Question

The radii of two right circular cylinders are in the ratio of 3:2 and their heights are in the ratio of 4:5. Calculate the ratio of their curved surface areas and also ratio of their volumes. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Let the radii of two cylinders be 3r and 2r respectively and their heights be 4h and 5h respectively. Let $S_1$ and $S_2$ be the curved surface Areas of the two cylinders and $V_1$ and $V_2$ be their corresponding volumes

$S_1$ = Curved Surface Area of the cylinder of height 4h and radius 3r

$=2\pi \times 3r\times 4h$

$=24\pi rh.\text{Sq. units}$.

$S_2$ = Curved Surface Area of the cylinder of height 5h and radius 2r

$=2\pi \times 2r\times 5h$.

$=20\pi rh\text{sq units}$.

$\therefore$ $\frac{S_1}{S_2}=\frac{24\pi rh}{20\pi rh}$

$\Rightarrow \frac{S_1}{S_2}=\frac{5}{6}$

$V_1$ = Volume of the cylinder of height 4 h and radius 3r

$=\pi \times (3r{)}^2\times 4h$

$=36\pi r^{2}h\text{cubic units}$

$V_2$ = Volume of the cylinder of height 5h and radius 2r

$=\pi \times (2r{)}^2\times 5h$

$=20\pi r^{2}h\text{cubic units}$

$\therefore \frac{V_1}{V_2}=\frac{36\pi r^{2}h}{20\pi r^{2}h}$

$\frac{V_1}{V_2}=\frac{9}{5}$