Question

Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio of the surface area of the small cylinder to the surface area of the large cylinder.

Answer 1

Answer:

4:25

Step-by-step explanation:

Given that,

r₁ = 15 inches, r₂ = 6 inches

The area of the cylinder is given by :

$A=2\pi rh+2\pi r^2$

The ratio of surface areas of two cylinders,

$\dfrac{S_2}{S_1}=\dfrac{2\pi r_2h_2+2\pi r_2^2}{2\pi r_1h_1+2\pi r_1^2}\\\\\dfrac{S_2}{S_1}=(\dfrac{r_2}{r_1})^2\\\\=\dfrac{6}{15}^2\\\\=\dfrac{4}{25}$

Hence, the required ratio is 4:25.