A toy is in the form of a right circular cone mounted on a hemisphere. If the height of the cone is twice the radius of the cone and the total height of the toy is 15 centimeters, what is the volume of the hemisphere in cubic centimeters? (The volume of a sphere is , where r is the radius)a)100andpi;/3b)125andpi;/3c)250andpi;/3d)500andpi;/3e)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?

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, where r is the radius)

a)
100π/3
b)
125π/3
c)
250π/3
d)
500π/3
e)
Cannot be determined

Correct answer is option 'C'. Can you explain this answer?

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A toy is in the form of a right circular cone mounted on a hemisphere....

A toy is in the form of a right circular cone mounted on a hemisphere
- Total height of the toy = 15 centimeter
Height of the cone = 2 * [radius of the cone]
The volume of a sphere = , where r is the radius

To Find: Volume of hemisphere

Approach

Let’s assume the radius of the hemisphere to be R.
- As the cone is mounted on the hemisphere, the
  
  Radius of the cone = Radius of the hemisphere = R
Now, we are given the relation that Height of the cone(let’s assume to be H) = 2 * R
Also, we know the total height of the cone = H + R = 15 centimeters

a. From the above equation, we can find the value of R

Working Out

Height of Cone(H) = 2R
Height of Toy = H + R = 2R + R = 3R = 15, i.e. R = 5 centimeters
Volume of hemisphere

Answer: C

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A toy is in the form of a right circular cone mounted on a hemisphere. If the height of the cone is twice the radius of the cone and the total height of the toy is 15 centimeters, what is the volume of the hemisphere in cubic centimeters? (The volume of a sphere is , where r is the radius)a)100π/3b)125π/3c)250π/3d)500π/3e)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?

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