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: ${\text{V}}_{\text{cylinder}}=\pi \times {\text{radius}}^2\times \text{height}$

Volume of Cube is given by: ${\text{V}}_{\text{cube}}={\text{edge}}^3$

Volume of Cube is given by ${\text{V}}_{\text{cuboid}}=\text{length}\times \text{breadth}\times \text{height}$

Therefore,

$\Rightarrow {\text{V}}_{\text{cylinder}}=\frac{22}{7}\times r^2\left(2r\right)=\frac{44}{7}{r}^3$
$\Rightarrow {\text{V}}_{\text{cube}}=(\frac{3}{4}r{)}^3=\frac{27}{64}{r}^3$

$\Rightarrow {\text{V}}_{\text{cuboid}}=r\times \frac{5}{4}r\times \frac{7}{3}r=\frac{35}{12}{r}^3$

Comparing the above volumes we get that ${\text{V}}_{\text{cube}}$ < ${\text{V}}_{\text{cuboid}}$ < ${\text{V}}_{\text{cylinder}}$