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 diameter 14 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 21 cm.
`["Assume "pi=22/7]`
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
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 sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
The total surface area of a hemisphere is how many times the square of its radius
