Question

A right circular cone and a right circular cylinder have equal base area. They also have the same curved surface area. If the height of the cylinder is 3 m, then the slant height of the cone is:
(a) 3
(b) 4
(c) 6
(d) 7

Answer 1

Hint: As it is given that the base area of the cone and the cylinder are equal and we know that both have circular bases, we can say that the radius of the bases are equal. We know that the curved surface area of the cylinder is equal to $2\pi rh$ and the curved surface area of the cone is $\pi rl$ , where l is equal to $\sqrt{{{r}^{2}}+{{h}^{2}}}$ . Now substitute the values in the formulas and equate the two to reach the answer.

Complete step-by-step answer:
We will start the solution to the above question by drawing the diagram of the situation given in the question.

As it is given that the base area of the cone and the cylinder are equal and we know that both have circular bases, we can say that the radius of the bases are equal and let it be r meters.
Now, we know that the curved surface area of the cylinder is equal to $2\pi rh$ .
$\text{CSA of cylinder}=2\pi rh=2\pi \times r\times 3=6\pi r$
Also, we know that the curved surface area of the cone is $\pi rl$ , where l is equal to $\sqrt{{{r}^{2}}+{{h}^{2}}}$ .
$\text{CSA of cone}=\pi rl$
Now as it is given that both have the same curved surface area, we will equate the two results. On doing so, we get
$\text{CSA of cylinder=CSA of cone}$
$\Rightarrow 6\pi r\text{=}\pi rl$
$\Rightarrow l=6m$
Therefore, the answer to the above question is option (c).

Note: The question is purely based on formulas. If you know the formulas of the curved surface area of the 3 dimensional figure mentioned in the question, then you just have to put the values and get the answer, so try to learn all the basic formulas related to 3 dimensional figures. Also, make sure that you don’t commit a calculation mistake.