Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use 3.14 π= ]
The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1% approximately
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and the volume of the cone (taking π = 22/7 ).
Write True or False and justify your answer:
If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
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.
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