Advertisements
Advertisements
प्रश्न
A sphere and a cube are of the same height. The ratio of their volumes is
पर्याय
3 : 4
21 : 11
4 : 3
11 : 21
Advertisements
उत्तर
In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of the cube be x units.
So, volume of the sphere (V1) = `4/3 pi (d/2)^3`
`=4/3 pi (x/2)^3`
`=4/3 pi (x^3 /8)`
`= (pi x^3)/6`
Volume of the cube (V2) = S3
= x3
So, to find the ratio of the volumes,
`V_1/V-2 = (pi x^3/6)/x^3`
` = pi /6`
` = ((22/7))/6`
`=11/21 `
Therefore, the ratio of the volumes of sphere and cube of equal heights is 11 : 21.
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 21 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 14 cm.
Find the surface area of a sphere of diameter 14 cm.
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
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.
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 cm
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
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 ______.
