Find the volume of the body obtained by rotating a right-angled triangle with a hypotenuse

| May 31, 2021 | education

Find the volume of the body obtained by rotating a right-angled triangle with a hypotenuse of 10 cm and an acute angle of 30 degrees around the smaller leg.

It is known from the condition that the figure of rotation is a right-angled triangle with a hypotenuse of 10 cm and an acute angle of 30 °. Rotation takes place around the smaller leg.

So, the body that we get as a result of rotation of a right-angled triangle with a hypotenuse of 10 cm and an acute angle of 30 ° around the smaller leg is a cone.

Let’s find the radius of the base – this is the second leg, we look for it as:

10 * cos 30 ° = 10 * √3 / 2 = 5√3.

And we can find the smaller leg as:

10 * sin 30 ° = 10 * 1/2 = 5 – this leg is the height of the cone.

Let’s apply the formula to calculate the volume:

V = 1/3 * Sosn. * H = 1/3 * π * (5√3) ^ 2 * 5 = 1/3 * π * 75 * 5 = 125π cm ^ 3.



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