A cone is having its base radius 12 cm and height 20 cm. If the top of thiscone is cut into form of a small cone of base radius 3 cm is removed, thenthe remaining part of the solid cone become a frustum. Calculate thevolume of the frustum.Radius 3 cmHeight 20 cm* Radius 12 cm
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the volume of the frustum = 2970 cm³
Step-by-step explanation:
A cone is having its base radius 12 cm and height 20 cm
Volume of original Cone = (1/3) πr²h
= (1/3)(π)12² * 20
= 960 π cm³
If the top of this cone is cut into form of a small cone of base radius 3 cm is removed
height of cone removed = h'
=> 3 /12 = h'/20
=> h' = 5
height of cone removed = 5 cm
Volume of cone removed = (1/3) (π)3² * 5
= 15π cm³
the volume of the frustum = 960 π - 15π
= 945 π cm²
= 945 * 22/7
= 135 * 22
= 2970 cm³
the volume of the frustum = 2970 cm³
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