The height of a circular cylinder is increase | vedclass

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Question

(A) Let the initial radius be $r$ and height be $h$. The initial lateral surface area is $A_1 = 2 \pi r h$.The new height $h' = 6h$. The base area is

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Let the initial radius be $r$ and height be $h$. The initial lateral surface area is $A_1 = 2 \pi r h$.The new height $h' = 6h$. The base area is $\pi r^2$. The new base area is $\frac{1}{9} \pi r^2 = \pi (r')^2$,which implies $(r')^2 = \frac{1}{9} r^2$,so $r' = \frac{1}{3} r$.The new lateral surface area is $A_2 = 2 \pi r' h' = 2 \pi (\frac{1}{3} r) (6h) = 2 \pi r h 	imes (\frac{1}{3} 	imes 6) = 2 \pi r h 	imes 2$.Thus,the lateral surface area increases by a factor of $2$.

The height of a circular cylinder is increased $6$ times and the base area is decreased to $\frac{1}{9}$ of its value. The factor by which the lateral surface area of the cylinder increases is

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