Abhishek has three containers: a)Cylindrical container A having radius r and

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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

Options:

A . A, B, C

B . B, C, A

C . C, A, B

D . cannot be arranged

Answer: Option B
:
B

Volume of Cylinder is given by: $V_{cylinder} = π \times {radius}^{2} \times height$
Volume of Cube is given by: $V_{cube} = {edge}^{3}$
Volume of Cube is given by $V_{cuboid} = length \times breadth \times height$
Therefore,
$\Rightarrow V_{cylinder} = \frac{22}{7} \times r^{2} (2 r) = \frac{44}{7} r^{3}$
$\Rightarrow V_{cube} = (\frac{3}{4} r)^{3} = \frac{27}{64} r^{3}$
$\Rightarrow V_{cuboid} = r \times \frac{5}{4} r \times \frac{7}{3} r = \frac{35}{12} r^{3}$
Comparing the above volumes we get that $V_{cube}$ < $V_{cuboid}$ < $V_{cylinder}$

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