Ramesh has three containers. A. Cylindrical container A having radius r and height h, B. Cylindrical container B having radius 2r and height 1 2 h. C. Cuboidal container C having dimensions r r h. The arrangement of the containers in the increasing order of their volumes is:

Ramesh has three containers. A. Cylindrical container A having ra…

MCQ

Ramesh has three containers.
$A.$ Cylindrical container $A$ having radius $r$ and height $h,$
$B.$ Cylindrical container $B$ having radius $2r$ and height $\frac{1}{2}$ $h.$
$C.$ 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
$B, C, A.$
✓
$C, A, B.$
D
cannot be arranged.

✓

Answer

Correct option: C.

$C, A, B.$

$(i)$ The volume of the cylindrical container having radius $r$ and height h $=\pi\text{r}^2\text{h}$
$(ii)$ The volume of the cylindrical container with radius $2r$ and height $\frac{1}{2}=\pi(2\text{r})^2\times\frac{1}{2}\text{h}$
$=\pi\times4\text{r}^2\times\frac{1}{2}\text{h}$
$=2\pi\text{r}^2\text{h}$
$(iii)$The volume of the cuboidal container having dimensions $r \times r \times h = r^2h$
From parts $(i), (ii)$ and $(iii),$ we have the following order $C, A, B.$