The radius of the cylinder base is 4 cm, and the axial cross-sectional area is 72 cm2. Find the volume of a cylinder.

| April 4, 2021 | education

Given: A cylinder where the base radius is BF = 4 cm and the axial sectional area (ie rectangle ABCD) is 72 cm². It is necessary to find the volume of the cylinder, which we denote by V.
To calculate the volume of a cylinder, we will use the formula V = π * R2 * H, where R is the radius of the base of the cylinder, H is the height of the cylinder. The radius of the cylinder base is known R = BF = 4 cm.
Let’s find the height of the cylinder H = AB, that is, the height of the rectangle ABCD, which is the axial section of the cylinder.
It is known that the area of ​​a rectangle can be calculated by the formula S = a * b, where a and b are the sides of the rectangle.
It can be seen from the figure that ВC is the diameter of the cylinder base. Therefore, BC = 2 * R = 2 * BF = 2 * 4 cm = 8 cm.
So, S = AB * BC = H * 8 cm = 72 cm², whence H = (72 cm²): (8 cm) = 9 cm.
Thus, V = π * (4 cm) ^ 2 * (9 cm) = π * (16 * 9) cm3 = 144 * π cm3.
Answer: 144 * π cm3.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.