Question

if the ratio of curved surface area and the total surface area of a cone is 3:4 then the ratio of height and radius of the cone is...
C the image que no. 51
Plz help me guys

Answer 1

Answer:

Option(2)

Step-by-step explanation:

Let the radius be r and height of the cone be h.

Given, Ratio of CSA and TSA is 3:4.

⇒ πrl/πr(l+r) = 3/4

⇒ l/l+r = 3/4

⇒ 4l = 3l + 3r

⇒ l = 3r

On Squaring both sides, we get

⇒ l² = 9r²

⇒ r² + h² = 9r²

⇒ 8r² = h²

⇒ (2√2)r² = h²

⇒ (r/h) = (2√2)/1

⇒ r : h = 2√2 : 1

Therefore, the ratio of height and radius = 2√2 : 1

Hope it helps!

Answer 2

Let the radius be r and height of the cone be h.

Given, Ratio of CSA and TSA is 3:4.

⇒ πrl/πr(l+r) = 3/4

⇒ l/l+r = 3/4

⇒ 4l = 3l + 3r

⇒ l = 3r

On Squaring both sides, we get

⇒ l² = 9r²

⇒ r² + h² = 9r²

⇒ 8r² = h²

⇒ (2√2)r² = h²

⇒ (r/h) = (2√2)/1

⇒ r : h = 2√2 : 1

Therefore, the ratio of height and radius = 2√2 : 1