XAT 2019 — QA & DI Question 3
A gold ingot in the shape of a cylinder is melted and the resulting molten metal molded into a few identical conical ingots. If the height of each cone is half the height of the original cylinder and the area of the circular base of each cone is one ï¬fth that of the circular base of the cylinder, then how many conical ingots can be made?
Answer & solution
- A
40
30
- C
60
- D
20
- E
10
Volume of a cylinder = π × (base area) × height
Volume of a cylinder = 1/3 × π × (base area) × height
Volume of a cone with same base and height as that of a cylinder is 1/3rd the volume of the cylinder.
If height of the cone is half that of the cylinder, volume will also become half. Also, if the base area is 1/5th the volume will also be 1/5th.
∴ Volume of the given cone = 1/3 × 1/2 × 1/5 = 1/30th the volume of the original cylinder.
∴ 30 such cones can be made from the original cylinder.
Alternately,
Let A and h be the base area and height of the cylinder.
Base area of the cone = A/5 and height = h/2
Volume of a cylinder (V) = πAh
Volume of a cylinder = 1/3 × π × A/5 × h/2 = πAh/30 = V/30
∴ Volume of the given cone is 1/30th the volume of the cylinder.
⇒ 30 such cones can be made from the original cylinder.
Hence, option (b).