Write True or False and justify your answer:
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the
volume of the sphere will be 6 : π.
Write True or False and justify your answer:
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.
Write True or False and justify your answer:
A cylinder and a right circular cone are having the same base and same height.
The volume of the cylinder is three times the volume of the cone.
Write True or False and justify your answer:
The volume of the largest right circular cone that can be fitted in a cube whose
edge is 2r equals to the volume of a hemisphere of radius r.
Write True or False and justify your answer:
If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.
Write True or False and justify your answer:
In a right circular cone, height, radius and slant height do not always be sides of a
right triangle.
Write True or False and justify your answer:
If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.
Write True or False and justify your answer:
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is
(A) 1 : 4 (B) 1 : 3 (C) 2 : 3 (D) 2 : 1
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