A spherical ball, 12 cm in diameter, is melted and cast into a conical mould, the base of which is 24 cm in diameter. What is the height of the cone?( in cm)Choices:- 4 6 8 10
Question
A spherical ball, 12 cm in diameter, is melted and cast into a conical mould, the base of which is 24 cm in diameter. What is the height of the cone?( in cm)Choices:- 4 6 8 10
Solution
To solve this problem, we need to use the formula for the volume of a sphere and a cone.
The volume of a sphere is given by the formula: V = 4/3 * π * r³ The volume of a cone is given by the formula: V = 1/3 * π * r² * h
Given that the diameter of the sphere is 12 cm, the radius (r) would be 6 cm.
So, the volume of the sphere is: V = 4/3 * π * 6³ = 288π cm³
The diameter of the base of the cone is 24 cm, so the radius (r) would be 12 cm.
We can set the volume of the sphere equal to the volume of the cone and solve for the height (h) of the cone:
288π = 1/3 * π * 12² * h 288 = 4 * 12 * h 288 = 48h h = 288 / 48 h = 6 cm
So, the height of the cone is 6 cm. The correct choice is 6.
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