The height of the cylinder is 8 cm, its total surface area is 130п cm². Find the area of the axial section of this cylinder.

Initially, we determine what the total surface area of the cylinder is equal to:
S = 2nRh + 2nR ^ 2 = 2nR (h + R).
Let’s substitute our data:
130p = 2nR (8 + R);
65 = R (8 + R);
R ^ 2 + 8R – 65 = 0.
Let’s solve this quadratic equation:
D = b ^ 2 – 4ac = 64 + 4 * 65 = 64 + 260 = 324.
√D = 18.
Find the roots of the equation:
R1 = (-8 + 18) / 2 = 5.
R2 = (-8 – 18) / 2 = -13 – not suitable.
We got that the radius of the base is 5 cm, then the length of the diameter is 10 cm, then the area of the axial section is equal to:
S1 = d * h = 10 * 8 = 80 cm2.
Answer: 80 cm2.