# Find the total surface area of the cylinder and its volume, if the base diameter is 8 cm, the diagonal of the axial section is 12 cm.

D = 8 cm.

d = 12 cm.

V – 7

Floor -?

The volume of the cylinder V is determined by the formula: V = P * R ^ 2 * h, where P is the number pi, R is the radius of the base of the cylinder, h is the height of the cylinder.

The total surface area of the cylinder Spol is determined by the formula: Spol = 2 * P * R ^ 2 + 2 * P * R * h.

Base radius R = D / 2.

R = 8 cm / 2 = 4 cm.

In the axial section of the cylinder, the plane forms a rectangle with sides D and h, the diagonal of which is d.

By the Pythagorean theorem d ^ 2 = D ^ 2 + h ^ 2.

h = √ (d ^ 2 – D ^ 2).

h = √ ((12cm) ^ 2 – (8cm) ^ 2) = 8.95cm.

V = 3.14 * (4 cm) ^ 2 * 8.95 cm = 449.6 cm ^ 3.

S floor = 2 * 3.14 * (4 cm) ^ 2 + 2 * 3.14 * 4 cm * 8.95 cm = 325.3 cm ^ 2.

Answer: V = 449.6 cm ^ 3, S floor = 325.3 cm ^ 2.