The radii of the two spheres are in the ratio 4:3. What is the ratio between their volumes?
- A36:27
- B25:64
- C64:36
- D64:27
Solution & Step-by-step Explanation
Let the radii of the two spheres be r
1
and r
2
.
Given:
r
2
r
1
=
3
4
The volume of a sphere is given by the formula V=
3
4
πr
3
.
Therefore, the ratio of their volumes is:
V
2
V
1
=
3
4
πr
2
3
3
4
πr
1
3
=(
r
2
r
1
)
3
Substituting the given values:
V
2
V
1
=(
3
4
)
3
=
27
64
So, the ratio of their volumes is 64:27.
1
and r
2
.
Given:
r
2
r
1
=
3
4
The volume of a sphere is given by the formula V=
3
4
πr
3
.
Therefore, the ratio of their volumes is:
V
2
V
1
=
3
4
πr
2
3
3
4
πr
1
3
=(
r
2
r
1
)
3
Substituting the given values:
V
2
V
1
=(
3
4
)
3
=
27
64
So, the ratio of their volumes is 64:27.