(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

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(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 $A_2 = 2 \pi r' h' = 2 \pi (\frac{1}{3} r) (6h) = 2 \pi r h \times (\frac{1}{3} \times 6) = 2 \pi r h \times 2$.Thus,the lateral surface area increases by a factor of $2$.

Competitive Quantitative Aptitude Mensuration Measurement of Volume and Surface Area

Medium

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

A
$2$
B
$\frac{1}{2}$
C
$\frac{2}{3}$
D
$\frac{3}{2}$

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Mensuration

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Measurement of Volume and Surface Area

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It is required to design a circular pipe such that water flowing through it at a speed of $7 \ m/min$ fills a tank of capacity $440 \ m^3$ in $10 \ min$. The inner radius of the pipe should be (in $m$):

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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

Similar Questions

The ratio of total surface area to lateral surface area of a cylinder whose radius is $80 \text{ cm}$ and height $20 \text{ cm}$ is: (in $:1$)

$A$ cubic metre of silver weighing $900\, Kg$ is rolled into a $16\, m$ long square bar. Find out the weight of an exact cube cut off from it.

Volume of the cylinder is $1650\, m^3$,whereas the surface area of its base is $78 \frac{4}{7}\, m^2$. Find out the height of the cylinder (in $m$).

$A$ cylindrical vessel of radius $4 \, cm$ contains water. $A$ solid sphere of radius $3 \, cm$ is lowered into the water until it is completely immersed. The water level in the vessel will rise by (in $cm$)

It is required to design a circular pipe such that water flowing through it at a speed of $7 \ m/min$ fills a tank of capacity $440 \ m^3$ in $10 \ min$. The inner radius of the pipe should be (in $m$):

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