Question

The ratio of the circumferences of two similar cylinders is 3:5. The lateral area of the smaller cylinder is 45π square feet. What is the lateral area of the larger cylinder, in terms of π? Use "pi" to represent π in the answer.

Answer 1

Given:

c1:c2 = 3:5

i.e r1:r2 = 3:5

A1 = 45π square feet

To find:

A2 =?

Step-by-step explanation:

Let A1, A2 be the lateral area of the cylinder.

The surface area of the cylinder is given by

A = 2πrh

The surface area of the smaller triangle is A1 is

A1 = 2π $r_1$ h = 45π     ...(1)

The surface area of the smaller triangle is A2 is

A2 = 2π $r_2$ h  = x      ...(2)

Divide eq (2) by eq (1)

$\displaystyle \frac{A_2}{A_1} = \frac{2 \pi r_1h}{2\pi r_2h}$

$\displaystyle \frac{x}{45\pi } = \frac{ 3}{5}$

x = 75π