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A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1cm and the height of the cone is equal to its radius. The volume of the solid is
- a)2π cm3
- b)3π cm3
- c)4π cm3
- d)π cm3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A solid is in the shape of a cone standing on a hemisphere with both t...
Radii of cone and hemisphere = r = 3 cm
Height of cone (h) = 1 cm
Volume of solid = Volume of cone + Volume of hemisphere
Height of cone (h) = 1 cm
Volume of solid = Volume of cone + Volume of hemisphere
Most Upvoted Answer
A solid is in the shape of a cone standing on a hemisphere with both t...
To find the volume of the solid, we need to find the volumes of the cone and the hemisphere separately and then add them together.
Volume of the cone = (1/3)πr^2h
Since the height of the cone is equal to its radius, the volume of the cone becomes:
Volume of the cone = (1/3)π(1^2)(1) = (1/3)π
Volume of the hemisphere = (2/3)πr^3
Since the radius of the hemisphere is 1cm, the volume of the hemisphere becomes:
Volume of the hemisphere = (2/3)π(1^3) = (2/3)π
Therefore, the total volume of the solid is:
Volume of the solid = Volume of the cone + Volume of the hemisphere = (1/3)π + (2/3)π = (3/3)π = π
So, the volume of the solid is π cubic cm.
Volume of the cone = (1/3)πr^2h
Since the height of the cone is equal to its radius, the volume of the cone becomes:
Volume of the cone = (1/3)π(1^2)(1) = (1/3)π
Volume of the hemisphere = (2/3)πr^3
Since the radius of the hemisphere is 1cm, the volume of the hemisphere becomes:
Volume of the hemisphere = (2/3)π(1^3) = (2/3)π
Therefore, the total volume of the solid is:
Volume of the solid = Volume of the cone + Volume of the hemisphere = (1/3)π + (2/3)π = (3/3)π = π
So, the volume of the solid is π cubic cm.
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