Question

Abhishek has three containers:

a)Cylindrical container A having radius r and height 2r
b)Cubical container B having its edge $\frac{3}{4}r$
c)Cuboidal container C having dimensions $r\times \frac{5}{4}r\times \frac{7}{3}r$

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 B

B, C, A

Volume of Cylinder is given by:
$V_{cylinder}=\pi \times radiu{s}^2\times \text{h}eight$

Volume of Cube is given by:
$V_{cube}=edg{e}^3$

Volume of Cube is given by:
$V_{cuboid}=\text{l}ength\times \text{b}readth\times \text{h}eight$

Therefore,

$\Rightarrow V_{cylinder}=\pi \times r^2\left(2r\right)=2\pi r^3$

$\Rightarrow V_{cube}=(\frac{3}{4}r{)}^3=\frac{27}{64}{r}^3$

$\Rightarrow V_{cuboid}=r\times \frac{3}{4}r\times \frac{7}{3}r=\frac{35}{12}{r}^3$

Comparing the above volumes we get that
$V_{cube}$ < $V_{cuboid}$ < $V_{cylinder}$

So the correct answer is Option B.