The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
A. 2 : 1
B. 1 : 1
C. 2 : 3
D. 1 : 2
Answers
Answer:
C.2:3
is the answer.
because height of the cylinder is twice the radius of sphere.
We know that, Volume of a sphere ,V1 = (4/3)πr³
Volume of a cylinder ,V2 = πr²h
If a cylinder circumscribes a sphere of radius r , then its base radius is ‘r’ and height is 2r.
Ratio between the volume of a sphere and volume of a circumscribing right circular cylinder , V1 : V2 :
V1/V2 = (4/3)πr³ / πr²h
= (4/3)πr³ / πr²(2r)
= (4/3)πr³ / 2πr³
= 4/3 / 2
V1/V2 = 4/3 / 2
V1/V2 = 4/3 × 1/2
V1/V2 = 2/3
V1 : V2 = 2 : 3
Hence the ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is 2 : 3.
Option (C) 2 : 3 is correct.
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