The radius of the base of the cone is 15 cm. The length of the generatrix of the cone is 50 cm.

The radius of the base of the cone is 15 cm. The length of the generatrix of the cone is 50 cm. Find the total surface area and volume of the cone.

The height of the cone h, the radius of the base r and the generatrix l form a right-angled triangle. Find the height of the cone:

h = √ (h ^ 2 – r ^ 2) = √ (50 ^ 2 – 15 ^ 2) = √ (2500 – 225) = √2275 = 5√91.

Base area:

Sop = nr ^ 2 = 3.14 * 15 ^ 2 = 706.5 cm ^ 2.

Side surface area:

S side = (2prl) / 2 = prl = 3.14 * 15 * 50 = 2355 cm ^ 2.

Full area S:

S = Sb + S side = 706.5 cm ^ 2 + 2355 cm ^ 2 = 3061.5 cm ^ 2.

Cone volume:

V = (1/3) * Sbn * h = (5√91 * 706.5) / 3 = 11232.63 cm ^ 3.

Answer: S = 3061.5 cm ^ 2, V = 11232.63 cm ^ 3.