Mango juice is contained in a bucket with a height of 35 cm and radii at the lower and upper ends of 14 cm and 21 cm, respectively. Calculate the cost of the juice at Rs. 25 per litre that will fill the bucket.

Question

Question

This question was previously asked in

MP Excise Constable Official paper (Held On: 24 Feb 2023 Shift 1)

Answer 1

Given:

Height (h) = 35 cm

Radius at lower end (r₁) = 14 cm

Radius at upper end (r₂) = 21 cm

Cost of juice = Rs. 25 per litre

Formula used:

Volume of frustum of cone = (1/3)πh(r₁² + r₂² + r₁r₂)

Where, r₁ and r₂ are the radii at the lower and upper ends, respectively.

1 litre = 1000 cm³

Calculations:

Volume = (1/3)π × 35 × (14² + 21² + 14 × 21)

⇒ Volume = (1/3) × 22/7 × 35 × (196 + 441 + 294)

⇒ Volume = (1/3) × 22/7 × 35 × 931

⇒ Volume = (1/3) × 110 × 931

⇒ Volume = 34,136.66 cm³

⇒ Volume in litres = 34,136.66 / 1000 = 34.136 litres

Cost = 34.136 × 25

⇒ Cost = Rs. 853.4

∴ The correct answer is option (2).

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