The height of the cone is 4cm and the diameter of the base is 6cm. Find the side surface of the cone.
| September 16, 2021 | education
On him:
AB = 4 cm – cone height.
AC = 6: 2 = 3 (cm) – radius of the base of the cone (R).
BC is the generator of the cone (L), we do not know its length yet.
The generator VS can be found by the Pythagorean theorem:
BC2 = AB2 + AC2.
BC2 = 16 + 9.
BC2 = 25.
BC = 5 (cm).
Let’s use the formula to calculate the area of the lateral surface of the cone:
S side. surface = πRL.
Substitute the data we know into the formula and get:
S side. surface = π x 3 x 5 = 15 π (cm2).
Answer: the area of the lateral surface of the cone is 15 π cm2.
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