The main section of the cylinder is square, the area of the base of the cylinder is 16P cm2

| April 18, 2021 | education

The main section of the cylinder is square, the area of the base of the cylinder is 16P cm2. Find the surface area of the cylinder. The height of the cone is 6 cm, the angle at the apex of the axial section is 120. Find: a) the area of the cone section by a plane passing through 2 generatrices, the angle between which is 30, b) the area of the lateral surface

1.

Knowing the area of ​​the base of the cylinder, we determine its radius.

Sbn = π * R ^ 2 = 16 * π cm2.

R = 4 cm.

Since the axial section of the cylinder is square, AB = h = 2 * R = 8 cm.

Then S side = 2 * π * R * h = 2 * π * 4 * 8 = 64 * π cm2.

Then the total surface area is equal to:

Sпов = 2 * Sсн + Sside = 2 * 16 * π + 64 * π = 96 * π cm2.

Answer: The total surface area is 96 * π cm2.

2.

The axial sectional area of ​​the cone is an isosceles triangle ABC with an apex angle of 120. The height of ВO is the bisector and median of triangle ABC. Then, in a right-angled triangle ABO, the angle ABO = 60, the angle OAB = 30.

The height of the ВO lies opposite the angle 30, then the hypotenuse of the triangle and the generatrix of the cone AB = 2 * 6 = 12 cm.

Forming BD = BE = AB = 12 cm.

Then Ssec = BD * BE * Sin30 / 2 = 12 * 12/4 = 36 cm2.

In a right-angled triangle AOB: OA ^ 2 = R ^ 2 = 144 – 36 = 108.

R = 6 * √3 cm.

Then S side = π * R * AB = π * 6 * √3 * 12 = 72 * π * √3 cm2.

Answer: Ssection = 36 cm2, Side = 72 * π * √3 cm2



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