A rectangle with a perimeter of 18 cm and an area of 18 cm squared rotates around

A rectangle with a perimeter of 18 cm and an area of 18 cm squared rotates around the larger side. Find the volume of the cylinder obtained by rotation.

Let’s call the rectangle ABCD, where AB = CD = x cm, BC = AD = y cm, then we write the following system of equations:
2 (x + y) = 18;
xy = 18;
x = 9 – y;
y (9 – y) = 18;
x = 9 – y;
y ^ 2 – 9y + 18 = 0.
Let’s find the discriminant:
D = 81 – 4 * 18 = 9, then y = (9 + 3) / 2 = 6, y = (9 – 3) / 2 = 3.
1) x = 3 cm.
We will rotate around a side with a length of 6 cm, then the base area will be equal to:
S = π * R ^ 2 = 9π cm2.
Let’s find the volume:
V = 9π * 6 = 54π cm3.
(the second answer is equal to the first, since they rotate around the larger side)
Answer: the volume of the cylinder is 54π cm3