Advertisements
Advertisements
Question
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Advertisements
Solution
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
RELATED QUESTIONS
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
Find the surface area of a sphere of radius 5.6 cm.
Find the surface area of a sphere of diameter 21 cm.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use ЁЭЬЛ = 3.14)
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
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.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
The ratio of the total surface area of a sphere and a hemisphere of same radius is
A sphere and a cube are of the same height. The ratio of their volumes 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
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
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 .
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 .
The volume of a sphere is 905 1/7 cm3, find its diameter.
A solid sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
