Answer:
The value of r is 6
Step-by-step explanation:
1. Here it is given that M is directly proportional to
�
3
r
3
. So this is case of direct proportion.
2. We can write in this way
�
2
�
1
=
�
2
3
�
1
3
M
1
M
2
=
r
1
3
r
2
3
or
�
2
�
1
=
(
�
2
�
1
)
3
M
1
M
2
=(
r
1
r
2
)
3
...1)
3. Where in equation 1)
�
1
=
160
M
1
=160
�
2
=
540
M
2
=540
�
1
=
4
r
1
=4
4. Again from equation 1), on putting respective value
540
160
=
(
�
2
4
)
3
160
540
=(
4
r
2
)
3
on solving L.H.S of above equation
27
8
=
(
�
2
4
)
3
8
27
=(
4
r
2
)
3
...2)
5. L.H.S of equation 2) can be written as
(
3
2
)
3
=
(
�
2
4
)
3
(
2
3
)
3
=(
4
r
2
)
3
So
3
2
=
�
2
4
2
3
=
4
r
2
So
�
2
=
4
×
3
2
=
6
r
2
=
2
4×3
=6
