Question

The radius of a cone is 5 cm and it's slant height is 13 cm. What is the perpendicular height of the cone?

Answer 1

Answer:

12 cm

Step-by-step explanation:

use Pythagoras theorem to find the height

${height}^{2} = {13}^{2} - {5}^{2} \\ {height}^{2} = 169 - 25 \\ {height }^{2} = 144 \\ height = \sqrt{144} \\ height = 12 \: cm$

Answer 2

Answer :

• The perpendicular height of the cone is 12 cm.

Given :

• The radius of a cone is 5 cm and it's slant height is 13 cm.

Solution :

• Radius of cone = 5 cm
• Slant Height of cone = 13 cm
• Height of cone = ?

Let height of cone be 'h'

★ Finding the height of cone by applying formula of Slant Height :

→ Slant Height = √(Radius)² + (Height)²

→ 13 = √(5)² + (h)²

→ 13 = √25 + h²

Squaring both the sides we get :

→ 169 = 25 + h²

→ 169 - 25 = h²

→ 144 = h²

→ h² = 144

Taking square root to both the sides :

→ h = √144

→ h = 12 cm

• Hence,the perpendicular height of the cone is 12 cm.