Question

Ramesh has three containers

(a) Cylindrical container A having radius $r$ and height $h$

(b) Cylindrical container B having radius $2r$ and height $\frac{1}{2}h$, and

(c) Cuboidal container C having dimensions $r\times r\times h$ The arrangement of the containers in the increasing order of their volumes is

• A. A,B,C
• B. B,C,A
• C. C,A,B
• D. cannot be arranged

Answer 1

The correct option is C

C,A,B

Finding the volume of the container A

Cylindrical container A having radius $r$ and height $h$

$\Rightarrow$The volume of the cylindeical container A $=$${\mathrm{\pi r}}^2\mathrm{h}$

Finding the volume of the container B

Cylindrical container B having radius $2r$ and height $\frac{1}{2}h$

$\Rightarrow$The volume of cylindrical container B $=$ $\mathrm{\pi }{\left(2\mathrm{r}\right)}^2\times \frac{\mathrm{h}}{2}=\mathrm{\pi }\times 4{\mathrm{r}}^2\times \frac{\mathrm{h}}{2}=2{\mathrm{\pi r}}^2\mathrm{h}$

Finding the volume of the container C

Cuboidal container C having dimensions $r\times r\times h$

$\Rightarrow$The volume of cuboidal container C $=\mathrm{l}\times \mathrm{b}\times \mathrm{h}=\mathrm{r}\times \mathrm{r}\times \mathrm{h}={\mathrm{r}}^2\mathrm{h}$

It is clearly visible that

$r^{2}h<{\mathrm{\pi r}}^2\mathrm{h}<2{\mathrm{\pi r}}^2\mathrm{h}$

Hence the correct option is C