# Solve the following problem?`?

the radii of 2 cyclinders are in the ratio 2:3 and their height are in the ratio 5:3. calculate

a)the ratio of their volumes and

b)the ratio of their surface areas?

Relevance
• 7 years ago

V1/V2 = pi * r1^2 * h1^2 / pi * r2^2 * h2 ^2

V1/V2 = 2^2 ^ 5 / 3^2 3

V1/V2 = 20/27

SA_1 / SA_2 = (2* pi * r1^2 + 2*pi*r1*h1) / (2* pi * r2^2 + 2*pi*r1 * h2)

SA_1 / SA_2 = r1* (r1 + h1) / r2* (r2 + h2)

SA_1/ SA_2 = 2(2 + 5) / 3*(3 + 3)

SA_1/ SA_2 = 14/27

Both of my answers assume that the cylinders are solid and that the ends would be included.

Lv 7
7 years ago

"the radii of 2 cylinders are in the ratio 2:3"

r₁/r₂ = 2/3

"their heights are in the ratio 5:3"

h₁/h₂ = 5/3

volume v = πr²h

v₁/v₁ = [πr₁²h₁]/[πr₂²h₂]

= (r₁/r₂)²(h₁/h₂)

= (2/3)²(5/3)

= 20/27

ratio of volumes = 20:27

:::::

Let r₁ = 1 and h₁ = 1, then r₂ = 1.5 and h₂ = 0.6

surface area a = 2πrh + 2πr²

a₁/a₂ = 4π/[2π1.5·0.6 + 2π1.5²]

= 2/3.15

= 40/63

ratio of surface areas = 40:63

• 7 years ago

a) (3/2)^2 * (3/5) = 27/20, so 20:27

b) I will assume the surface does NOT include the base, then (3/2)*(3/5) = 9/10, so 10:9

• 7 years ago

r1 = 2k, r2 = 3k, h1=5p, h2 = 3p where k and p are constants

a) Ratios of volume: pi (2k)^2(5p) : pi(3k)^2(3p) => 20: 27

b) Ratios of surface area : 2 pi (2k)(5p) : 2 pi (3k) (3p) => 10:9

• 7 years ago

ratio of thier area is 87.92/113.04

ratio of their volume =62.8/84.78