If the radius of a right circular cone is increased by 20% and its height is decreased by 25%, then the volume of the right circular cone will be increased by:
- A15%
- B12%
- C10%
- D8%
Solution & Step-by-step Explanation
The volume of a right circular cone is given by the formula:
V=
3
1
πr
2
h
Let the initial radius be r and the initial height be h.
New radius (r
′
) = r+0.20r=1.2r
New height (h
′
) = h−0.25h=0.75h
The new volume (V
′
) is:
V
′
=
3
1
π(r
′
)
2
h
′
=
3
1
π(1.2r)
2
(0.75h)
V
′
=
3
1
π(1.44r
2
)(0.75h)
V
′
=(1.44×0.75)×(
3
1
πr
2
h)
V
′
=1.08×V
The percentage increase in volume is:
Percentage Increase=(1.08−1)×100%=8%
V=
3
1
πr
2
h
Let the initial radius be r and the initial height be h.
New radius (r
′
) = r+0.20r=1.2r
New height (h
′
) = h−0.25h=0.75h
The new volume (V
′
) is:
V
′
=
3
1
π(r
′
)
2
h
′
=
3
1
π(1.2r)
2
(0.75h)
V
′
=
3
1
π(1.44r
2
)(0.75h)
V
′
=(1.44×0.75)×(
3
1
πr
2
h)
V
′
=1.08×V
The percentage increase in volume is:
Percentage Increase=(1.08−1)×100%=8%