The axial sectional area of the cylinder is 120 and the radius of the base of the cylinder is 7.5.

The axial sectional area of the cylinder is 120 and the radius of the base of the cylinder is 7.5. Find the diagonal of the axial section of the cylinder.

The axial cross-sectional area of ​​a cylinder is nothing more than the area of ​​a rectangle;
The area of ​​a rectangle is equal to the product of the sides of this rectangle: S = a * b (1);
The radius of the base of the cylinder will be equal to half of one of the sides of the axial section of the cylinder (assume sides a), then a = 2 * r (2), where r is the radius of the base of the cylinder;
Substitute the data into formula (2) and find the side a:
a = 2 * 7.5 = 15;
From formula (1) we express side b:
b = S / a (3);
Substitute the data into formula (3) and find the side b
b = 120/15 = 8;
The diagonal of the axial section of a cylinder is the same as the diagonal of a rectangle;
The diagonal of a rectangle can be found by the Pythagorean theorem (a ^ 2 + b ^ 2 = c ^ 2), where a and b are the sides of the rectangle and c is the diagonal of the rectangle:
c = (a ^ 2 + b ^ 2) ^ 0.5 (4);
Substitute the values ​​into formula (4) and find the diagonal:
c = (15 ^ 2 + 8 ^ 2) ^ 0.5 = 17;
Answer: the diagonal of the axial section of the cylinder is 17;