Question

select the correct answer from each drop - down menu.
consider the two cylinders.
the volumes of these two cylinders are
if another cross section is taken at a the areas of the cross sections will be equal.
(options: equal, similar, not equal)

Explanation:

Step1: Analyze cylinder volume formula

The volume of a cylinder is given by $V = \pi r^2 h$, where $r$ is the radius and $h$ is the perpendicular height of the cylinder.
For both cylinders, $r=7$ and perpendicular $h=16$.

Step2: Compare the two volumes

Substitute values into the formula:
For the right cylinder: $V_1 = \pi \times 7^2 \times 16$
For the oblique cylinder: $V_2 = \pi \times 7^2 \times 16$
Thus $V_1 = V_2$.

Step3: Analyze cross-section areas

Cross-sections parallel to the base of a cylinder (right or oblique) are circles with radius equal to the cylinder's base radius $r=7$. The area of each cross-section is $A = \pi r^2$, so all such cross-sections have equal area regardless of position.

Answer:

The volumes of these two cylinders are equal.
If another cross section is taken at the same perpendicular distance from the base, the areas of the cross sections will always be equal.