The area of the base of the cylinder is 4 cm2, the area of the axial section is 24 cm2, what is the volume of the cylinder.

The volume of the cylinder is found by the formula:
V = SH,
where S is the area of ​​the base, H is the height of the cylinder / length of the generatrix.
1. Since the axial section is a rectangle whose sides are equal to the diameter of the base and the length of the generatrix, we first find the diameter of the base.
The area of ​​the circle that lies at the base of the cylinder is found by the formula:
S = πR ^ 2,
where R is the radius of this circle.
πR ^ 2 = 4;
R ^ 2 = 4 / π;
R = √4 / π = 2 / √π = 2√π / π (cm).
Then the base diameter will be equal to:
D = 2R = 2 * 2√π / π = 4√π / π (cm).
2. Let the axial section be a rectangle ABCD, then AB = CD = H, AD = BC = D = 4√π / π.
The area of ​​a rectangle is equal to the product of its length and width, then:
Sc = H * D;
4√πH / π = 24;
4√πH = 24π;
H = 24π / 4√π;
H = 6π / √π = 6π√π / π = 6√π (cm).
3. Find the volume of the cylinder:
V = 4 * 6√π = 24√π (cm ^ 3).
Answer: V = 24√π cm ^ 3.