The height of the cone is 5cm; the generatrix of the cone is 7cm. Find the radius of the base and its volume.
| April 7, 2021 | education
The volume of the cone is calculated by the formula: V = 1 / 3Sb. * h;
The S of the base is piR ^ 2. We need to find the radius.
Consider a triangle, the legs of which are the radius and height, and the generatrix is the hypotenuse.
R = √ (l ^ 2 – h ^ 2) = √ (7 ^ 2 – 5 ^ 2) = √ (49 – 25) = √24 cm;
Substitute the resulting radius into the formula for finding the area of the base:
Sb = pi * √24 ^ 2 = 24pi cm2;
V = 1/3 * 24pi * 5 = 40pi cm3.
Answer: 40pi cm3.
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