Advertisements
Advertisements
प्रश्न
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.
पर्याय
True
False
उत्तर
This statement is True.
Explanation:
Let r be the radius of the sphere and cylinder.
Given that height of the cylinder = diameter of the sphere.
`\implies` h = 2r
According to the question,
Volume of a sphere = `2/3` × volume of cylinder
`\implies 4/3 pir^3 = 2/3 xx pir^2 xx 2r` ...[∵ h = 2r]
`\implies 4/3 pir^3 = 4/3 pir^3`
Hence, the volume of a sphere is equal to two-third of the volume of a cylinder.
APPEARS IN
संबंधित प्रश्न
Find the volume of a sphere whose radius is 7 cm.
`["Assume "pi=22/7]`
Find the volume of a sphere whose radius is 0.63 m.
`["Assume "pi=22/7]`
A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?
`["Assume "pi=22/7]`
The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?
The diameter of a coper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
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 π = 3.14]
