Multiple choice

A solid hemisphere is attached to the base of the right circular cone of diameter 20 cm and height 10 cm if this object is to be inscribed in a right circular cylinder then find the vacant space left in the cylinder?

  1. 500 π cm3

  2. 2000 π cm3

  3. 100 π cm3

  4. 1000 π cm3

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cone diameter 20 (r=10), height 10. Hemisphere radius 10. Cylinder radius 10, height 10+10=20. Cylinder volume = pi * 10^2 * 20 = 2000pi. Object volume = (1/3)pi*10^2*10 + (2/3)pi*10^3 = (1000/3)pi + (2000/3)pi = 1000pi. Vacant space = 2000pi - 1000pi = 1000pi.

AI explanation

To find the vacant space, we subtract the combined volume of the solid hemisphere and the right circular cone from the volume of the cylinder. The cylinder has a radius of 10 cm and a total height of 20 cm, giving a volume of 2000 pi, while the combined volume of the cone and hemisphere is 1000 pi. Subtracting these volumes gives a vacant space of 1000 pi cubic centimeters.

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