The rectangle, the sides of which are 15 cm and 5 cm, rotate first around the larger

| June 10, 2021 | education

The rectangle, the sides of which are 15 cm and 5 cm, rotate first around the larger side and then around the smaller one. Calculate the ratio of the volumes of the resulting cylinders.

The volume of the cylinder is calculated by the formula V = Sb. * h (Sbase is the area of the base of the cylinder, h is the height of the cylinder).

Sosn. = ПR ^ 2 (П = 3.14; R – base radius).

V = ПR ^ 2 * h.

1) If we rotate the rectangle around the larger side, then the height of the cylinder is h = 15 cm, and the radius of the base of the cylinder is R = 5 cm.

V1 = P * 5 ^ 2 * 15 = P * 25 * 15 = 375 P (cm ^ 3).

2) If we rotate the rectangle around the smaller side, then the height of the cylinder is h = 5 cm, and the radius of the base of the cylinder is R = 15 cm.

V1 = P * 15 ^ 2 * 5 = P * 225 * 5 = 1125 P (cm ^ 3).

3) V2 / V1 = (1125 P) / (375 P) = 3.

Answer. The ratio of volumes V1 ^ V2 = 1: 3.



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