Find the volume of a cone of height 3 cm and slant height 5 cm?

Given:

Height of the cone, h = 3 cm

Slant height, l = 5 cm

Concept Used:

The volume of a cone is given by the formula:

Volume = (1/3) × π × r² × h

To find the radius (r), we use the Pythagoras theorem on the cone:

l² = r² + h²

⇒ r² = l² - h²

Calculation:

l = 5 cm, h = 3 cm

Using r² = l² - h²

 r² = 5² - 3²

 r² = 25 - 9

 r² = 16 ⇒ r = √16 = 4 cm

Now, substitute in the volume formula:

Volume = (1/3) × π × r² × h

Volume = (1/3) × 3.14 × 4² × 3

Volume = (1/3) × 3.14 × 16 × 3

Volume = (1/3) × 150.72

Volume = 50.24 cm³