the surface of the cube is double then of surface area of a sphere then ratio of their volume is About the author Lyla
Answer: Let the radius of the sphere be r and side of cube be a. Since, Surface area of the sphere = Surface area of cube 4πr 2 =6a 2 2πr 2 =3a 2 a 2 = 3 2πr 2 a=r 3 2π Therefore, V 2 V 1 = a 3 3 4 π×r 3 = 3(r 3 2π ) 3 4π×r 3 = 3( 3 2π 3 2π ) 4π = 3 2π 2 = 12 2π 1 = 6 π 1 Hence, the required ratio is 1: 6 π . Reply
Answer:
Let the radius of the sphere be r and side of cube be a.
Since,
Surface area of the sphere = Surface area of cube
4πr
2
=6a
2
2πr
2
=3a
2
a
2
=
3
2πr
2
a=r
3
2π
Therefore,
V
2
V
1
=
a
3
3
4
π×r
3
=
3(r
3
2π
)
3
4π×r
3
=
3(
3
2π
3
2π
)
4π
=
3
2π
2
=
12
2π
1
=
6
π
1
Hence, the required ratio is 1:
6
π
.