The height of the cone is 6 cm and the generatrix is 10 cm find: the radius of the base -?

| June 20, 2021 | education

The height of the cone is 6 cm and the generatrix is 10 cm find: the radius of the base -? Axial cross-sectional area -? Surface area V-?

The OBC triangle, formed by the height, the generatrix and the radius of the circle, is rectangular, then, according to the Pythagorean theorem, ОВ ^ 2 = ВС ^ 2 – ОC ^ 2 = 100 – 36 = 64.

ОВ = R = 8 cm.

Let’s calculate the area of ​​the base of the cone. Sop = n * R ^ 2 = n * 64 cm2.

The area of ​​the lateral surface of the cone is equal to: Side = n * R * L = n * R * BC = n * 8 * 10 = n * 80 cm2.

Then Spov = Sbok + Sosn = n * 80 + n * 64 = n * 144 cm2.

The axial section of the cone is an isosceles triangle ABC, which is divided by the height OC into two equal triangles AOC and BOC.

Then Ssec = 2 * Svos = 2 * OВ * OС / 2 = 8 * 6 = 48 cm2.

Answer: The radius of the base is 8 cm, the total area is 144 cm2, the cross-sectional area is 48 cm2.



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