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A cylinder, whose height is two-thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.
- a)4 cm
- b)5 cm
- c)3 cm
- d)6 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A cylinder, whose height is two-thirds of its diameter, has the same v...
Given:
Height of the cylinder = 2/3 of its diameter
Volume of the cylinder = Volume of the sphere
To find: Radius of the base of the cylinder
Let's solve this step by step.
1) Formula for the volume of a cylinder is given by:
Volume = πr^2h, where r is the radius and h is the height.
2) Formula for the volume of a sphere is given by:
Volume = 4/3πr^3, where r is the radius of the sphere.
3) Since the volume of the cylinder is equal to the volume of the sphere, we can equate the two formulas:
πr^2h = 4/3πr^3
4) Canceling out π and dividing both sides by r^2, we get:
h = 4/3r
5) Given that the height of the cylinder is 2/3 of its diameter, which means h = 2/3d, where d is the diameter of the cylinder.
6) Substituting h = 2/3d in the equation from step 4, we get:
2/3d = 4/3r
7) Canceling out 2/3 on both sides and solving for r, we have:
d = 2r
r = d/2
8) Substituting r = d/2 in the equation from step 6, we get:
2/3d = 4/3(d/2)
9) Canceling out 2/3 on both sides and solving for d, we have:
1 = 4/3
This is not possible.
10) Therefore, the given information is inconsistent, and we cannot determine the radius of the base of the cylinder.
Height of the cylinder = 2/3 of its diameter
Volume of the cylinder = Volume of the sphere
To find: Radius of the base of the cylinder
Let's solve this step by step.
1) Formula for the volume of a cylinder is given by:
Volume = πr^2h, where r is the radius and h is the height.
2) Formula for the volume of a sphere is given by:
Volume = 4/3πr^3, where r is the radius of the sphere.
3) Since the volume of the cylinder is equal to the volume of the sphere, we can equate the two formulas:
πr^2h = 4/3πr^3
4) Canceling out π and dividing both sides by r^2, we get:
h = 4/3r
5) Given that the height of the cylinder is 2/3 of its diameter, which means h = 2/3d, where d is the diameter of the cylinder.
6) Substituting h = 2/3d in the equation from step 4, we get:
2/3d = 4/3r
7) Canceling out 2/3 on both sides and solving for r, we have:
d = 2r
r = d/2
8) Substituting r = d/2 in the equation from step 6, we get:
2/3d = 4/3(d/2)
9) Canceling out 2/3 on both sides and solving for d, we have:
1 = 4/3
This is not possible.
10) Therefore, the given information is inconsistent, and we cannot determine the radius of the base of the cylinder.
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Community Answer
A cylinder, whose height is two-thirds of its diameter, has the same v...
Let the radius o f the cylinde r be /'em.
So, diameter of the cylinder = 2r
So, diameter of the cylinder = 2r
∴ Height of the cylinder = 2/3(2r) = 4r/3
Volume of the cylinder = Volume of the sphere of radius 4 cm
⇒ 
⇒ r3 = 43 ⇒ r = 4 cm.
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A cylinder, whose height is two-thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.a)4 cmb)5 cmc)3 cmd)6 cmCorrect answer is option 'A'. Can you explain this answer?
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