Find the volume of the figure if the radius of the hemisphere and cylinder is 6 inches and the height of the cylinder is 12 inches. Find the volume in terms of pi.
assuming you have a hemisphere atop a cylinder, they both have the same radius.
So, just plug your numbers into the usual volume formulas.
720π in3
the answer is d
To find the volume of the figure, we need to break it down into two components: the hemisphere and the cylinder. We'll calculate the volumes of each component separately and then add them together to get the total volume.
1. Volume of Hemisphere:
The volume of a hemisphere can be calculated using the formula V = (2/3) * pi * r^3, where r is the radius of the hemisphere.
Given the radius of the hemisphere is 6 inches, substitute this value into the formula:
V_hemisphere = (2/3) * pi * 6^3
V_hemisphere = (2/3) * pi * 216
V_hemisphere = 144 * pi cubic inches
2. Volume of Cylinder:
The volume of a cylinder can be calculated using the formula V = pi * r^2 * h, where r is the radius of the base and h is the height of the cylinder.
Given the radius of the cylinder is 6 inches and the height is 12 inches, substitute these values into the formula:
V_cylinder = pi * 6^2 * 12
V_cylinder = pi * 36 * 12
V_cylinder = 432 * pi cubic inches
3. Total Volume:
To get the total volume of the figure, add the volumes of the hemisphere and the cylinder together:
Total Volume = V_hemisphere + V_cylinder
Total Volume = 144 * pi + 432 * pi
Total Volume = (144 + 432) * pi
Total Volume = 576 * pi cubic inches
Therefore, the volume of the figure in terms of pi is 576 pi cubic inches.