A rectangle with sides of 3 cm and 4 cm rotates around a straight line passing through the midpoints

| August 11, 2021 | education

A rectangle with sides of 3 cm and 4 cm rotates around a straight line passing through the midpoints of its large sides, which body of revolution turns out to find the diagonal of its axial section and the area of the base of this body of revolution.

When you rotate the rectangle around a straight line passing through the midpoints of its large sides, you get a cylinder. The axial section of such a cylinder will be this rectangle. To find the diagonal of this triangle, you need to consider the triangle that it forms a rectangle with two sides. This triangle is rectangular, and the diagonal in it is its hypotenuse. Hence, it can be found by the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs. Find the diagonal:

√ (3² + 4²) = √ (9 + 16) = √25 = 5 cm.

The base of this cylinder is a circle with a diameter of 4 cm.Its area can be calculated by the formula

S = ¼ πd², where d is the diameter of the circle.

Find the area of ​​the base:

S = ¼ π * 4² = 4π ≈ 12.6 cm².

Answer: when you rotate the rectangle, you get a cylinder; the diagonal of the axial section of the cylinder is 5 cm; the base area of ​​the cylinder is approximately 12.6 cm².



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