The spherical and the cylindrical candles shown have the same radius and the same height.
A photo of a cylindrical and a spherical candle is shown.
The volume of the cylindrical candle is 6 cubic centimeters. What is the volume of the spherical candle? Explain.
Enter the correct answers in the boxes.
Show Hints
Volume: . The volume of a sphere is the volume of the cylinder with the same radius and the same height.
Hint: The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. The volume of a sphere is given by the formula V = (4/3)πr^3. Since the cylindrical and spherical candles have the same radius and height, their volumes are equal.
Given that the volume of the cylindrical candle is 6 cubic centimeters, we can use this information to solve for the volume of the spherical candle.
Using the formula for the volume of a cylinder, we have:
6 = πr^2h
Since the cylindrical and spherical candles have the same radius and height, their volumes are equal, so:
6 = (4/3)πr^3
Now, we can set these two equations equal to each other and solve for the volume of the spherical candle.
Equating the two volume formulas gives:
6 = (4/3)πr^3
Solving for r gives:
r = (3/4)^(1/3)
Now, we can calculate the volume of the sphere using the formula V = (4/3)πr^3:
V = (4/3)π((3/4)^(1/3))^3
Calculating this expression will give us the volume of the spherical candle.