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(D) Let the radius of the base of both the cone and the cylinder be $r$. Since they have the same base area,their radii are equal.Let the slant height

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Let the radius of the base of both the cone and the cylinder be $r$. Since they have the same base area,their radii are equal.Let the slant height of the cone be $l$ and the height of the cylinder be $h = 2 \, m$.The curved surface area of the cone is given by $A_{cone} = \pi r l$.The curved surface area of the cylinder is given by $A_{cylinder} = 2 \pi r h$.According to the problem,$A_{cone} = A_{cylinder}$.Therefore,$\pi r l = 2 \pi r h$.Dividing both sides by $\pi r$ (since $r 
eq 0$),we get $l = 2h$.Substituting $h = 2 \, m$,we get $l = 2 	imes 2 = 4 \, m$.Thus,the slant height of the cone is $4 \, m$.

$A$ cone and a cylinder having the same area of the base have also the same area of curved surfaces. If the height of the cylinder is $2 \, m$,find the slant height of the cone (in $m$).

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