Question

Find the height of a conical tank if the base radius and slant height of the cone are in the ratio 5 : 7 and the curved surface area is 990 cm².

1. 3√6 cm
2. 9√6 cm
3. 10√6 cm
4. 6√6 cm

Answer 1

Correct Answer - Option 4 : 6√6 cm

Given:

The ratio of the base radius and slant height of the conical tank is 5 : 7.

The curved surface area of the conical tank is 990 cm².

Formula used:

The curved surface area of the cone = πrl

l² = r² + h²

where r = Base radius of the cone, l = Slant height of the cone and h = Height of the cone

Calculation:

According to the question,

r/l = 5/7

Let r be 5x and l be 7x.

Again, according to the question,

πrl = 990

⇒ (22/7) × 5x × 7x = 990

⇒ 5x² = 45

⇒ x² = 9

⇒ x = 3

So, r = 5 × 3

⇒ 15 cm

l = 7 × 3

⇒ 21 cm

We know, (l)² = (r)² + (h)²

⇒ (21)² = (15)² + (h)²

⇒ 441 = 225 + h²

⇒ h² = 216

⇒ h = 6√6

∴ The height of the cone is 6√6 cm.