The diameter and height of a cylindrical container are shown.
A cylinder has a height of 7 inches and diameter of 16 inches.
The container is filled completely with cheese sauce. Which of these represents the total number of cubic inches of cheese sauce in the container?
f 2π⋅82+2π⋅8⋅7
g π⋅162⋅7
h π⋅82⋅7
j 2π⋅162+2π⋅16⋅7
The correct answer is (h) π⋅82⋅7.
To find the volume of the cylinder (i.e. the total number of cubic inches of cheese sauce in the container), we need to use the formula:
V = πr^2h
where r is the radius (which is half the diameter) and h is the height.
In this case, the radius is 8 inches (since the diameter is 16 inches), and the height is 7 inches.
Plugging these values into the formula, we get:
V = π(8^2)(7) = π(64)(7) = 448π
So the total number of cubic inches of cheese sauce in the container is 448π. Simplifying this gives us option (h), π⋅82⋅7.