Find the surface area of the cone whose height is 12 cm and the radius of the base is 9 cm.

Decision:

1.) S = π × R × (R + l), where

S is the total surface area of the cone;

R is the radius of the base of the cone;

l – generatrix of the cone;

π is a constant equal to ≈3.14.

The value of the generator l is not enough for the solution. Let’s find her.

Since H is the height of the cone, then triangle BOC is rectangular, CO = H = 12 cm, OB = R = 9 cm, CB is the hypotenuse of triangle BOH. CB = l.

Now we have all the necessary quantities: calculate S:

S = π × 9 cm × (9 cm + 15 cm) = 216π cm² ≈ 678.24 cm².

Answer: 216π ≈ 678.24 cm².