An equilateral triangle of side 14 centimeters is revolved about an altitude to form a cone. what is the number of cubic centimeters in the volume of the cone? express your answer to the nearest whole number, without units.

To solve this problem, let us recall that the formula for the volume of a cone is:

V = (1 / 3) π r^2 h

where,

r = is the radius of the cone

h = is the height of the cone

Now since the equilateral triangle is rotated about the altitude (center of the triangle figure), therefore we can say that the radius and height is:

r = 7 cm

h = 14 cm

Hence, the volume of the cone is:

V = (1 / 3) π (7 cm) ^2 (14 cm)

V = 228.67 π cm^3

or

V = 718.38 cm^3