Question

Consider the two cylinders. Cross-section of two cylinders is shown. Regular cylinder with radius 7 units and height 16 units. Circular cross-section is highlighted at the middle. Oblique cylinder with radius 7 units. Circular cross-section is highlighted at the middle. The volumes of these two cylinders are ___ . If another cross-section is taken at a different height, the areas of the cross sections will be equal.

a. V₁ < V₂, True
b. V₁ > V₂, False
c. V₁ = V₂, True
d. V₁ = V₂, False

Answer 1

The volumes of the two cylinders are equal.

Step-by-step explanation:

The formula to calculate the volume of a regular cylinder is V = A imes h, where V is the volume, A is the area of the circular cross-section, and h is the height of the cylinder. In this case, the regular cylinder has a radius of 7 units and a height of 16 units. The formula becomes:

V₁ = π imes (7)^2 imes 16

To calculate the volume of the oblique cylinder, we use the same formula. Since the cross-section at a different height has the same area, the volume remains the same. Therefore, the volume of the oblique cylinder is also V₂ = π imes (7)^2 imes 16.

Therefore, the volumes of both cylinders are equal. The answer is V₁ = V₂, True.