A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
A. 1 : 2 : 3
B. 2 : 1 : 3
C. 2 : 3 : 1
D. 3 : 2 : 1
Answers
Given : A cone, a hemisphere and a cylinder stand on equal bases and have the same height.
height of cone, h = height of cylinder = base radius = r
Volume of a right circular cone , V1 = (1/3)πr²h
Volume of a hemisphere ,V2 = (2/3)πr³
Volume of a cylinder , V3 = πr²h
⇒ V1 : V2 : V3
= (1/3)πr²h : (2/3)πr³ : πr²h
= (1/3)πr²(r) : (2/3)πr³ : πr²(r)
= 1/3πr³ : 2/3πr³ : πr³
= 1/3 : 2/3 : 1
= 1 : 2 : 3
V1 : V2 : V3 = 1 : 2 : 3
Hence, the ratio of their volumes is 1 : 2 : 3
Option (A) 1 : 2 : 3 is correct.
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Answer:
Step-by-step explanation:⇒ V1 : V2 : V3
= (1/3)πr²h : (2/3)πr³ : πr²h
= (1/3)πr²(r) : (2/3)πr³ : πr²(r)
= 1/3πr³ : 2/3πr³ : πr³
= 1/3 : 2/3 : 1
= 1 : 2 : 3
V1 : V2 : V3 = 1 : 2 : 3