Question

Two right circular cylinders of equal volumes have their radii in the ratio
2 : 5. What is the ratio of their heights?

Answer 1

Let :

◈ For first cylinder,

➠ Radius of = r

➠ Height = h

◈ For 2nd cylinder

➠ Radius = R

➠ Height = H

Given :

• Volume of two right circular cylinder is same (let V)
• Radius of both are in ratio 2:5

To find :

Ratio of height of cylinder (h :H)

Formula used :

Volume of cylinder = πr²h

Solution :

◈ Volume of first cylinder = Volume of second cylinder

➠ π r² h = π R²H

➠ (r/R)² = H/h

➠ (2/5)² = H/h

➠ (4/25) = H/h

➠ h/H = 25/4

➠ h : H = 25 : 4

ANSWER :

Ratio of height = 25 : 4

Answer 2

Step-by-step explanation:

volume of cylinder = πr²h

r is the radius and h is the height

the ratio of radii of the cylinders is = 2:5

let radius of first cylinder = r1

height of first cylinder = h1

volume will be π(r1)²h1

radius of second cylinder = r2

height of second cylinder = h2

volume will be = π(r2)²h2

volume of both cylinder is equal

π(r1)²h1 = π(r2)²h2

(r1)²h1 = (r2)²h2

r1 = 2x ; r2 = 5x

(2x)²h1 = (5x)²h2

4x²h1 = 25x²h2

4h1 = 25h2