Question

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.

Answer 1

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