Question

The volume of a right circular cylinder is 250 cm³. If the height of the cylinder is equal to the diameter of its base, then find its height.

Answer 1

Given:

Volume of cylinder V = 250π cm³

Height of the cylinder = diameter of the base

h = 2r

To find:

Height h

Step 1: Write the formula for the volume of a cylinder

V = πr²h

Step 2: Substitute the given condition h = 2r

V = πr²(2r) = 2πr³

Step 3: Substitute the value of volume

2πr3 = 250π

Cancel π from both sides:

2r³ = 250

Step 4: Solve for r

r³ = 125

r = 5 cm

Step 5: Find the height

h = 2r

= 2 × 5 

= 10 cm