If altitude of a circular cylinder is increased 12 times and the base area is decreased to one ninth...

Question

The altitude of a circular cylinder is increased 12 times and the base area is decreased to one ninth of its value.
How much would be the change in surface area of new cylinder?

Answer 1

let the original height = h and base radius = R.
let the new height = 12h and new radius = r.
now pi*r^2 = pi*R^2/9 ,r/R => 1/3 i.e 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

Answer 2

In a circular cylinder , we have top area, lateral area and base area
Let us calculate the total surface of the cylinder, as follows:
top area = A, base area = A and lateral area = 2 x Pi x r x h = 2 x pi x sqroot ( A/Pi) x h
For the new coditions, top a = 1/9 A , base a = 1/9 A and
lateral area = 2 x pi x r x 12h = 2 x pi x sqroot ( 1/9 pi ) x 12 h = 8 x pi x sqrrot (A/pi) x h
Therefore,
top and base areas are decreased to 1/9 of the original value
the lateral surface is increased 4 (four times)

Answer 3

6*pi*r*l-16*pi*r*r/9 The original surface area being 2*pi*r*l+2*pi*r*r and the new being 2*pi*(r/3)*12*l +2*pi*(r/3)^2