Multiple choice

Height of a solid cylinder is $10$ cm and diameter $8$ cm. Two equal conical holes have been made from both the ends of cylinder. If the diameter of the hole is $6$ m and height $4$ cm. The volume of the remaining portion is

  1. $24 \pi \ \text{cm}^3$
  2. $36 \pi \ \text{cm}^3$
  3. $72 \pi \ \text{cm}^3$
  4. $136 \pi \ \text{cm}^3$
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D Correct answer
AI explanation

The volume of a cylinder is pi*r^2*h, so using the radius of 4 cm and height of 10 cm gives a volume of pi * 4^2 * 10 = 160*pi cubic cm. The volume of a cone is (1/3)*pi*r^2*h, and since there are two conical holes with a radius of 3 cm and height of 4 cm, their combined volume is 2 * (1/3) * pi * 3^2 * 4 = 24*pi cubic cm. Subtracting the volume of the conical holes from the cylinder's volume gives 160*pi - 24*pi = 136*pi cubic cm.

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