Question

The volume of a right circular cone is \[1232c{m^3}\] and its vertical height is \[24cm\]. Its curved surface area is:
A). \[154c{m^2}\]
B). \[550c{m^2}\]
C). \[604c{m^2}\]
D). \[704c{m^2}\]

Answer 1

Hint: In the given question, we have been given a problem involving the use of a right circular cone. We have been given the volume and the vertical height of the cone. We have to find the curved surface area of the cone. To do that, we are going to write the formula of volume, and find the radius of the cone. Then, we find the curved surface area by using the appropriate formula.

Formula used:
We are going to use the formula of volume and curved surface area of a cone, which is:
\[V = \dfrac{1}{3}\pi {r^2}h\] and \[CSA = \pi r\sqrt {{r^2} + {h^2}} \]

Complete step by step solution:

The given volume of the cone is \[1232c{m^3}\]. The height is given to be \[24cm\].
We know, \[V = \dfrac{1}{3}\pi {r^2}h\]. Putting in the values,
\[1232 = \dfrac{1}{3} \times \dfrac{{22}}{7} \times {r^2} \times 24\]
Taking all the constants to one side,
\[\dfrac{{1232 \times 3 \times 7}}{{22 \times 24}} = {r^2}\]
Simplifying, we get,
\[{r^2} = 49\]
So, \[r = 7cm\]
Now, putting the values into the formula \[CSA = \pi r\sqrt {{r^2} + {h^2}} \], we have,
\[CSA = \dfrac{{22}}{7} \times 7 \times \sqrt {{7^2} + {{24}^2}} \]
Hence, the curved surface area is \[550c{m^2}\].
Thus, the correct option is (B).

Note: In the given question, we had to find the curved surface area of a cone. We were given the volume and height of the cone. We calculated it by applying the formula of volume to find the radius, then used the value of radius and height to calculate the curved surface area. So, it is very important that we know all the formulae and the results of the formulae.