The altitude of a circular cylinder is increased 12 times and the base area is decreased to one nint

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11 Nov 2016 Surface Area

The altitude of a circular cylinder is increased 12 times and the base area is decreased to one ninth of its value. The factor by which the lateral surface area of the cylinder increases is:

OPtion

1) 2/3
2) 1/2
3) 3/2
4) 2
5) 3/2
6) 4
7) 3
8) 5/2
9) 5
10)None of these

Solution

let the original height = h & base radius = R
Let the new radius = r and the new height be 12h
Now, pi r^2 = pi R^2/9 => r/R = ⅓ => R=3r
Original lateral surface area / new lateral surface area = 2 pi *3r*h/2 pi*r*12h
new lateral surface area = 4* Original lateral surface area

Option 6)

Correct Option: 6 Best Solution (3)

G.S.Kantharao   8 years AGO

Lateral surface area= 2πrh
When height increased by 12times and base area is reduced by 1/9 times then r=r/3,h=12h then LSA= 2*π*r*12h/3= 4times.
Hence my option is 6.

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Pragati Rode   8 years AGO

Let the initial altitude of circular cylinder be l and base radius be r
new altitude of cylinder = 12* l

new base area = (pi * r^2)/9

new base radius = r/3

Earlier lateral surface area = 2* pi* r* l

New lateral surface area = 2 * pi * (r/3) * (12 * l) = 2*pi*r*l * 4
so the lateral surface area of circular cylinder increased by a factor of 4
so the option is 6

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Jagriti Priya   8 years AGO

lateral surface area of cylinder = 2*3.14*r*h
r = radius, h = height of cylinder
let H and R are height and radius of new cylinder.
as area of base is decreased by one ninth of previous = 3.14*R*R = (3.14*r*r)/9
therefore R = r/3
now h is increased by 12 times , H = 12h
now lateral surface area of new cylinder = 2*3.14*R*H
= 2*3.14*r/3*12h = 4(2*3.14*r*h) = 4 times increases.

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