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
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.
A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
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.
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.
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.
Find the radius of a sphere whose surface area is 154 cm2.
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 of the cone.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2
