A spherical ball of 8 cm diameter is melted into a cone with base 20 cm in diameter. Find its height.
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area of spherical ball = pie x r square
=22/7 * 4 = 12.57
area of spherical ball = area of cone = 1/2 * radius * height
12.57 = 1/2 * 10 * h
h = 12.57 * 2 / 10
h = 2.514 cm
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This is a question testing the concept of volume.
The formulas are as below:
Sphere Volume = 4/3πr³
Volume of a cone = h/3πr²
The radius of the spherical ball = 8/2 = 4 cm
The volume of the spherical ball :
= 4/3 × 3.14 × 4² = 66.99 cm³
the volume of a cone = volume of the spherical ball.
radius of the cone = 20/2 = 10 cm
66.99 = 1//3 × 10² × h
66.99 = 33.33h
h = 66.99/33.33
h = 2.01 cm
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