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

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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 Cubeis 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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