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 given by the formula V = πr^2h, where r is the radius and h is the height. Since the radius and height of both candles are the same, we can set up the following equation:
6 = πr^2h
Since the radius and height are the same for both candles, the radius and height of the spherical candle will also be r and h. The volume of a sphere is given by the formula V = (4/3)πr^3. Therefore, the volume of the spherical candle can be calculated using the radius r that we found from the cylindrical candle's volume:
V = (4/3)πr^3
V = (4/3)π(6/πh)^3
V = (4/3)π(216/π^3)
V = 288/π^2
V ≈ 91.7 cubic centimeters
Therefore, the volume of the spherical candle is approximately 91.7 cubic centimeters.