If the volume of spheres are 27: 8, then their ratio of surface areas is:
- A3:2
- B4:9
- C2:3
- D9:4
Solution & Step-by-step Explanation
Let the radii of the two spheres be R
1
and R
2
.
The formula for the volume of a sphere is V=
3
4
πr
3
.
Given the ratio of their volumes:
V
2
V
1
=
3
4
πR
2
3
3
4
πR
1
3
=
8
27
(
R
2
R
1
)
3
=
8
27
Taking the cube root on both sides:
R
2
R
1
=
2
3
The formula for the surface area of a sphere is A=4πr
2
.
The ratio of their surface areas is:
A
2
A
1
=
4πR
2
2
4πR
1
2
=(
R
2
R
1
)
2
A
2
A
1
=(
2
3
)
2
=
4
9
Therefore, the ratio of their surface areas is 9:4.
1
and R
2
.
The formula for the volume of a sphere is V=
3
4
πr
3
.
Given the ratio of their volumes:
V
2
V
1
=
3
4
πR
2
3
3
4
πR
1
3
=
8
27
(
R
2
R
1
)
3
=
8
27
Taking the cube root on both sides:
R
2
R
1
=
2
3
The formula for the surface area of a sphere is A=4πr
2
.
The ratio of their surface areas is:
A
2
A
1
=
4πR
2
2
4πR
1
2
=(
R
2
R
1
)
2
A
2
A
1
=(
2
3
)
2
=
4
9
Therefore, the ratio of their surface areas is 9:4.