Question

select the correct answer from each drop - down menu. consider the two cylinders. the volumes of these two cylinders are drop - down menu. if another cross section is taken at a different height, the areas of the cross sections will drop - down menu be equal.

Explanation:

Step1: Analyze the first cylinder (right circular cylinder)

The volume of a right circular cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. For the first cylinder, \( r = 7 \) and \( h = 16 \), so its volume is \( V_1=\pi\times7^2\times16=\pi\times49\times16 = 784\pi \).

Step2: Analyze the second cylinder (oblique cylinder)

The volume of an oblique cylinder is also given by \( V=\pi r^2 h \), where \( h \) is the perpendicular height (the distance between the two circular bases, which is the same as the height of the right cylinder in this case, since the radius is the same and the perpendicular height is 16). So the volume of the oblique cylinder \( V_2=\pi\times7^2\times16 = 784\pi \). Thus, the volumes of the two cylinders are equal.

Step3: Analyze the cross - sectional areas

For a right circular cylinder, the cross - section (a circle) at any height has an area \( A=\pi r^2 \), where \( r = 7 \), so \( A=\pi\times7^2 = 49\pi \). For an oblique cylinder, when we take a cross - section at a given height, the cross - section is still a circle with the same radius (because the radius of the circular bases is 7 and the cross - section is parallel to the bases). So, if another cross - section is taken at a different height, the areas of the cross - sections will always be equal (because the radius of the circular cross - section remains the same for both cylinders at any height, so \( A=\pi r^2 \) is the same for both at any height).

Answer:

The volumes of these two cylinders are equal. If another cross section is taken at a different height, the areas of the cross sections will always be equal.