Advertisements
Advertisements
Question
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
Options
π : 2
π : 3
π : 4
π : 6
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 sphere and volume of a cube. 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 sphere (V1) = `(4/3) pi (d/2)^3`
` = (4/3)pi(d^3/8)`
=`(pi d^3)/6`
Volume of a cube (V2) = S3
`=d^3`
Now, the ratio of the volume of sphere to the volume of the cube = `V_1/V_2`
`V_1/V_2=(((pi d^3)/6))/d^3`
So, the ratio of the volume of sphere to the volume of the cube is π : 6 .
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 14 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.
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
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?
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.
A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Find the radius of the sphere whose surface area is equal to its volume .
How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?
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 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 number of cones recast. `("Take" pi =22/7)`
Find the volume and surface area of a sphere of diameter 21 cm.
There is surface area and volume of a sphere equal, find the radius of sphere.
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.
A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?
