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.
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.
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