A rectangle, one of the sides of which is 7 cm and a diagonal of 25 cm, rotates around the larger side. Calculate the volume of the formed body of revolution.
From the right-angled triangle ABC, by the Pythagorean theorem, we determine the length of the side AB.
AB ^ 2 = AC ^ 2 – BC ^ 2 = 25 ^ 2 – 7 ^ 2 = 576.
AB = 24 cm.
Then the rotation of the rectangle occurs around the side of 24 cm, as a result of rotation, a cylinder with a height AB = 24 cm and a radius of a circle at the base of BC = 7 cm will be obtained.
Let’s calculate the volume of the formed cylinder.
V = S main * h.
V = n * R ^ 2 * h = n * BC ^ 2 * AB = n * 49 * 24 = n * 1176 cm3.
Answer: The volume of the pyramid is equal to n * 1176 cm3.
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