SSC CPO 2023 PYQ — Question 140

The correct answer is Option 1 i.e. 5 : 14.

Given:

Slant height (l) = 29 cm, and height = 20 cm

T.S.A of cone = πr(l + r)

Volume of cone = 1/3πr²h

here, r = radius, and h = height

We know that,

l² = h² + r²

⇒ r² = l² - h²

⇒ r² = 29² - 20²

⇒ r² = 841 - 400

⇒ r² = 441

⇒ r = 21

T.S.A of cone = πr(l + r) 

⇒ π × 21 × (29 + 21) = π × 21 × 50 

Volume of cone = 1/3πr²h

⇒ 1/3 × π × 21² × 20

Ratio = (π × 21 × 50)/(1/3 × π × 21² × 20)

⇒ (21 × 50)/(1/3 × 21² × 20)

⇒ 50/(1/3 × 21 × 20)

⇒ 150/(21 × 20) = 5/14 = 5 : 14