. A cone and a sphere have equal heights and equal
volumes. The ratio of their radii is :
Answers
Given : A cone and a sphere have equal heights and equal volumes.
To find : ratio of their radii
Solution:
Let say Height of Sphere & cone = h
Radius of Sphere = Height of Sphere/2 = h/2
Radius of Cone = r
Volume of Sphere = (4/3)π(radius)³ = (4/3)π (h/2)³
= πh³/6
Volume of Cone = (1/3)πr²h
= (1/3)πr²h
(1/3)πr²h = πh³/6
=> 2r² = h²
=> h = √2 r
ratio of Cone radius : Ratio of sphere radius
= r : h/2
= r : √2 r/2
= 2r : √2
=> √2 : 1
The ratio of their radii is : √2 : 1
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Step-by-step explanation:
Given A cone and a sphere have equal heights and equal
volumes. The ratio of their radii is
- Given a cone and a sphere have equal volume. So v1 = v2
- Therefore volume of cone = volume of sphere
- 1/3 π r^2 h = 4/3 π r^3
- So we get h = 4r
- Now substituting in the given equation we get
- 1/3 π r^2 4r = 4/3 π r^3
- So we get
- r^3 = r^3
- 1 = 1
- Therefore the ratio of their radii is 1:1
Reference link will be
https://brainly.in/question/2637240