Advertisements
Advertisements
प्रश्न
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Advertisements
उत्तर
In the given problem, we are given a sphere inscribed in a cube. So, here we need to find the ratio between the volume of a cube and volume of sphere. This means that the diameter of the sphere will be equal to the side of the cube. Let us take the diameter as d.
Here,
Volume of a cube (V1) = s3
= d3
Volume of a sphere (V2) `=(4/3)pi (d/2)^3`
`=(4/3) pi (d^3/8)`
`=(pid^3)/6`
Now, the ratio of the volume of sphere to the volume of the cube = `V_1/V_2`
`V_1/V_2 = d^3/(((pi d^3)/6))`
`= 6/pi`
So, the ratio of the volume of cube to the volume of the sphere is `6 : pi` .
APPEARS IN
संबंधित प्रश्न
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
Find the surface area of a sphere of radius 14 cm.
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
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?
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
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.
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :
- the radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
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.
The total surface area of a hemisphere of radius r is
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm .
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
A spherical cannon ball, 28 cm in diameter is melted and recast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.
