A right-angled triangle with leg 3 and hypotenuse 5 rotates around an axis drawn through

| September 26, 2021 | education

A right-angled triangle with leg 3 and hypotenuse 5 rotates around an axis drawn through the vertex of the right angle parallel to the hypotenuse. find the surface of the resulting body of revolution.

The resulting figure is visible in the figure. The surface area of ​​the resulting body will be equal to the sum of the lateral surfaces of the two cones (upper and lower) and the area of ​​the lateral surface of the cylinder.

We calculate the second leg of the triangle: √ (5² – 3²) = √ (25 – 9) = √16 = 4.

The area of ​​the lateral surface of the cone is equal to Sk = ПRL (R is the radius of the base, L is the generatrix).

The radius of the body of revolution will be the height of a right-angled triangle drawn from the vertex of the right angle.

h = (a * b) / c (a, b – legs, c – hypotenuse).

h = (3 * 4) / 5 = 12/5 = 2.4.

This means that the area of ​​the lateral surface of the upper cone is Sk = П * 2.4 * 4 = 9.6П.

Similarly, the lateral surface area of ​​the lower cone is Sk = П * 2.4 * 3 = 7.2П.

The area of ​​the lateral surface of the cylinder is Sc = 2ПRh = 2 * P * 2.4 * 5 = 24П.

Therefore, the body surface area is: S = 9.6П + 7.2П + 24П = 40.8П.



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