A right-angled triangle with an angle of 60 degrees and a hypotenuse of 10√3 cm rotates around

A right-angled triangle with an angle of 60 degrees and a hypotenuse of 10√3 cm rotates around the larger leg. Find the volume of the resulting body of revolution.

Body of revolution, cone.
The volume of the cone is calculated:
V = 1 / 3Pi * H * R ^ 2.
Formula designations:
H – height, this is the larger leg of a right-angled triangle;
R is the smaller leg.
The smaller leg – R, lies opposite an angle of 30 degrees, therefore it is equal to 1/2 of the hypotenuse. We get the following formula:
R = 10√3 / 2 = 5√3.
We can find the second leg H by the Pythagorean theorem:
H = √ (300 – 75);
H = 15.
We know the values of R and H for finding the volume.
Let’s substitute:
V = 1 / 3Pi * 15 * (5√3) ^ 2;
V = 75.
Answer: V = 75