Advertisements
Advertisements
प्रश्न
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
Advertisements
उत्तर
Let edge of the cube = a
Volume of the cube = a × a × a = a3
The sphere, which exactly fits in the cube, has radius = `a/2`
Therefore, volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx (a/2)^3`
= `4/3 xx 22/7 xx a^3/8`
= `11/21 a^3`
Volume of cube : Volume of sphere
= `a^3 : 11/21 a^3`
= `1 : 11/21`
= 21 : 11
संबंधित प्रश्न
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
Find the radius of the sphere whose surface area is equal to its volume .
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the volume of remaining solid
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
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 ______.
