Question

Ramesh has three containers.

a) Cylindrical container A having radius ${}^{\prime }{r}^{\prime }$ and height ${}^{\prime }{h}^{\prime }$

b) Cylindrical container B having radius ${}^{\prime }2r^{\prime }$ 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

a) The volume of the cylindrical container having radius r and height h $=\pi r^{2}h$

b) The volume of the cylindrical container having radius 2r and height $\frac{1}{2}$ h =$2\pi r^{2}h$

c) The volume of the cuboidal container C having dimensions r x r x h = $r^{2}h$

Clearly, volume of cuboidal container < volume of the cylindrical container having radius r and height h < volume of the cylindrical container having radius 2r and height $\frac{1}{2}$ h.