The spherical and the cylindrical candles shown have the same radius and the same height.
The volume of the cylindrical candle is 6 cubic centimeters. What is the volume of the spherical candle? Explain.
The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius and h is the height. Since the cylindrical candle has a volume of 6 cubic centimeters, we can set up the equation as:
6 = πr^2h
Since the spherical candle has the same radius and height as the cylindrical candle, the radius and height of the sphere can be considered as r as well. The formula for the volume of a sphere is V = (4/3)πr^3. Therefore, the volume of the spherical candle is:
V = (4/3)πr^3 = (4/3)πr^2r = 4πr^2 * (1/3)r = 4πr^2h = 4 * 6 = 24 cubic centimeters.
Thus, the volume of the spherical candle is 24 cubic centimeters.