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A cone whose height is half of its radius is melted to from a hemi-sphere. Find the ratio of the radius of the hemi-sphere to that of cone.
- a)1:3
- b)4:1
- c)1:4
- d)1:2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cone whose height is half of its radius is melted to from a hemi-sph...
volume will remains constant. So,
V = 1/3*22/7*r2*r/2 (volume of cone) and V = 2/3*22/7*R3 (volume of hemisphere)
So, R/r = 1:4
V = 1/3*22/7*r2*r/2 (volume of cone) and V = 2/3*22/7*R3 (volume of hemisphere)
So, R/r = 1:4
Most Upvoted Answer
A cone whose height is half of its radius is melted to from a hemi-sph...
Given:
Height of the cone = (1/2) radius of the cone
To find:
Ratio of radius of the hemisphere to that of cone
Solution:
Let the radius of the cone be ‘r’ and its height be ‘h’.
Given, h = (1/2)r
Volume of the cone = (1/3)πr²h
= (1/3)πr²(1/2)r
= (1/6)πr³
Volume of the hemisphere = (2/3)πr³
Since the material of the cone is used to form the hemisphere,
(1/6)πr³ = (2/3)πr³
r = √(6/2) = √3
Radius of the hemisphere = (2/3)r = (2/3)√3
Ratio of radius of the hemisphere to that of cone
= [(2/3)√3]/√3
= 2/3
Therefore, the ratio of the radius of the hemisphere to that of cone is 1:4 (option C).
Height of the cone = (1/2) radius of the cone
To find:
Ratio of radius of the hemisphere to that of cone
Solution:
Let the radius of the cone be ‘r’ and its height be ‘h’.
Given, h = (1/2)r
Volume of the cone = (1/3)πr²h
= (1/3)πr²(1/2)r
= (1/6)πr³
Volume of the hemisphere = (2/3)πr³
Since the material of the cone is used to form the hemisphere,
(1/6)πr³ = (2/3)πr³
r = √(6/2) = √3
Radius of the hemisphere = (2/3)r = (2/3)√3
Ratio of radius of the hemisphere to that of cone
= [(2/3)√3]/√3
= 2/3
Therefore, the ratio of the radius of the hemisphere to that of cone is 1:4 (option C).
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A cone whose height is half of its radius is melted to from a hemi-sphere. Find the ratio of the radius of the hemi-sphere to that of cone.a)1:3b)4:1c)1:4d)1:2Correct answer is option 'C'. Can you explain this answer?
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