The area of the lateral surface of the cone is 32π cm2, the radius of its base is 4.
December 28, 2020 | education
| The area of the lateral surface of the cone is 32π cm2, the radius of its base is 4. Find the height and angle between the height and its generatrix.
A cone with a generatrix L and a base radius R has a lateral surface area
S = PiRL.
By condition
Pi * 4L = 32Pi, whence
L = 8 cm.
By the Pythagorean theorem, we find the height of the cone
H = (L ^ 2 – R ^ 2) 0.5 = (8 ^ 2 – 4 ^ 2) ^ 0.5 = 48 ^ 0.5 = 6.93 cm.
The angle between the height and the generatrix is 30 °, since the leg R is equal to half of the hypotenuse L.
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