Question

The volume of a right circular cylinder can be obtained from its curved surface area by multiplying it by its:
(a) $\dfrac{\text{Radius}}{2}$
(b) \[\dfrac{2}{\text{Radius}}\]
(c) \[\text{height}\]
(d) \[2\times \text{Height}\]

Answer 1

Hint: Assume that the radius and height of the right circular cylinder is ‘r’ and ‘h’ respectively. Use the formula for volume of cylinder: $V=\pi {{r}^{2}}h$, where ‘V’ is the volume. Now, use the formula for curved surface area of the cylinder: $C.S.A=2\pi rh$, where C.S.A is the curved surface area. Divide the volume of the cylinder by its curved surface area and cancel the common terms. The dimension or expression left after simplifying is the required answer.

Complete step-by-step answer:
Let us assume that the radius and height of the right circular cylinder is ‘r’ and ‘h’ respectively.

Therefore, the Volume (V) of this cylinder is given by:
\[V=\pi {{r}^{2}}h.......................(i)\]
Also, the curved surface area (C.S.A) of this cylinder is given by:
$C.S.A=2\pi rh.....................(ii)$
Now, dividing equation (i) by equation (ii), we have,
$\dfrac{V}{C.S.A}=\dfrac{\pi {{r}^{2}}h}{2\pi rh}$
Cancelling the common terms, we get,
$\dfrac{V}{C.S.A}=\dfrac{r}{2}$
By cross-multiplication, we get,
$V=\dfrac{r}{2}\times C.S.A$
Clearly, we can see that the volume of the cylinder is $\dfrac{\text{Radius}}{2}$ times the curved surface area of the cylinder.
Hence, option (a) is the correct answer.

Note: Do not use the formula for total surface area of the cylinder, as we will get the wrong answer. Remember that the unit of volume is cubic units while the unit of area is square units. In the above solution, we have divided the volume by the curved surface area. We may also divide the curved surface area by the volume and take its reciprocal to get the relation: $V=\dfrac{r}{2}\times C.S.A$. The final answer will not change on simplification.