Question

What is the ratio of the volume of a cube to that of a sphere which will fit inside it?

Answer 1

Answer:

The ratio of  volume of a cube to that of a sphere which will fit inside it is 6 : π

Step-by-step explanation:

Given :  

Sphere fits inside the cube.

Let the side of a cube be 'a’  

Radius of a sphere , r = side of a cube/2 = a/2

r = a/2

Volume of cube(V1) / Volume of Sphere(V2) = a³ / (4πr³/3)

V1/V2 = a³ / (4πr³/3)

V1/V2 = a³ / (4π(a/2)³/3)

[r = a/2]

V1/V2 = a³ /(4π × (a³/8)/3)

V1/V2 = a³ /(4πa³/8)/3)

V1/V2 = a³ /(a³π/2)× 1/3)

V1/V2 = a³ /(a³π/6)

V1/V2 = 6a³ / (πa³)

V1/V2 = 6 / π

V1 : V2 = 6 : π

Hence, the ratio of  volume of a cube to that of a sphere which will fit inside it is 6 : π

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

✨HOLA!!!!✨

The diameter of the sphere will be same as the side of the cube if the sphere exactly fits in the cube .

So, let's take the diameter of the side of the cube as l.

Volume of the cube (V1) =l^3

Volume of the sphere (V2) =

$(4 \div 3)\pi(l \div 2) {}^{3}$

∴ V1:V2

l^3 : (4/3)π(l/2)^3

l^3:(4/3)π(l^3/8)

l^3:(π(l)^3)/6

6:π

HOPE IT HELPS UHH #CHEERS