if base radius of a right circular cylinder is Halved keeping the height same find the ratio of the volume of the reduced cylinder to that of the original cylinder
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Step-by-step explanation:
Correct option is C)
Let the radius of the cylinder is r and height is h
∴ Volume of the cylinder = πr
2
h
According to the question new radius is half of the initial radius
∴New radius=
2
r
Height is h.
∴New volume of the cylinder =
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If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
A
1:2
B
2:1
C
1:4
D
4:1
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Correct option is C)
Let the radius of the cylinder is r and height is h
∴ Volume of the cylinder = πr
2
h
According to the question new radius is half of the initial radius
∴New radius=
2
r
Height is h.
∴New volume of the cylinder = π(
2
r
)
2
h=π
4
r
2
h
∴ The ratio of the new volume of the cylinder and initial volume of the original cylinder=
πr
2
h
π
4
r
2
h
=
4
1
∴ Ratio =1:4.