Q. 244.0( 8 Votes )
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 is
A. 1 : 2
B. 2 : 1
C. 1 : 4
D. 4 : 1
Given: Radius of the base of a right circular cylinder is halved, keeping the height the same.
Let initial Radius of Right Circular Cylinder be ‘r’.
∴ Radius of the Cylinder after its radius is halved is ‘ ’
Let ‘h’ be the height of the both the cylinders.
Let V1 be the volume of the initial Cylinder.
Let V2 be the volume of the Cylinder after the initial Cylinders base radius is halved.
Volume of the Cylinder is given by: πr2h
∴ V1:V2 = π(r1)2h : π(r2)2h
∴ V1:V2 = π(r)2h : π(r/2)2h
⇒ V1:V2 = 1:
⇒ V1:V2 = 4:1
Thus, ratio of the volume of the cylinder thus obtained to the volume of original is 4:1.
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