To find the amount of wax needed to make a cone-shaped candle, we need to calculate the volume of the cone. The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
where V is the volume, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cone.
Substituting the given values, we get:
V = (1/3) * π * (2 cm)^2 * 6 cm
V = (1/3) * π * 4 cm^2 * 6 cm
V = (1/3) * π * 24 cm^3
V = 8π cm^3
Therefore, the volume of the cone-shaped candle is 8π cubic centimeters. This is also the amount of wax needed to make the candle.
To obtain a numerical approximation of this value, we can use the approximation π ≈ 3.14:
V ≈ 8 * 3.14 ≈ 25.12 cubic centimeters
So, approximately 25.12 cubic centimeters of wax is needed to make the cone-shaped candle.