A cylinder with a base area of 4n and a sine of the angle between the generatrix of the cylinder

| June 17, 2021 | education

A cylinder with a base area of 4n and a sine of the angle between the generatrix of the cylinder and the diagonal of its axial section equal to 0.2 is inscribed in the ball. Find the ratio of the surface area of the ball to the area of the base of the cylinder.

Since, by condition, the area of the circle at the base of the cylinder is equal to: Vbase = n * r ^ 2 = n * 4 cm2.

Then r ^ 2 = 4, r = 2 cm.

Determine the area of the base of the cylinder.

Sop = n * r ^ 2 = n * 2 ^ 2 = n * 4 cm2.

ОА = 2 cm, then AD = 2 * OA = 2 * 2 = 4 cm.

BC = AD = 4 cm.

Since, by condition, SinBAC = 0.2, then SinBAC = BC / AC = 0.2.

AC = ВС / SinBAC = 4 / 0.2 = D = 20 cm.

R = AC / 2 = 10 cm.

Let us determine the surface area of the ball.

Sball = 4 * n * R ^ 2 = 4 * n * 100 = n * 400 cm2.

Let’s define the area ratio.

Sball / Sbn = n * 400 / n * 4 = 100.

Answer: The area ratio is 100.



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