Question

determining true statements about the oblique cylinder
the volume of the oblique cylinder is 24 ft³.
which statements are true? check all that apply.
☐ the height of the cylinder is 3.4 ft.
☐ the diameter of the cylinder is about 4.5 ft.
☐ the diameter of the cylinder is about 3 ft.
☐ the radius of the cylinder is about 6 ft.
☐ a right cylinder with the same height and radius as this oblique cylinder would also have a volume of 24 ft³.

Explanation:

Step1: Confirm height of the cylinder

The diagram labels the perpendicular height as 3.4 ft, so this is the height used for volume calculations.

Step2: Recall cylinder volume formula

The volume of any cylinder (right or oblique) is $V = \pi r^2 h$, where $V$ is volume, $r$ is radius, $h$ is perpendicular height.

Step3: Solve for radius

Substitute $V=24$, $h=3.4$ into the formula:
$$24 = \pi r^2 (3.4)$$
$$r^2 = \frac{24}{3.4\pi} \approx \frac{24}{10.68} \approx 2.25$$
$$r \approx \sqrt{2.25} = 1.5 \text{ ft}$$

Step4: Calculate diameter

Diameter $d = 2r \approx 2 \times 1.5 = 3 \text{ ft}$

Step5: Verify right cylinder volume

The volume formula applies to both right and oblique cylinders with the same radius and perpendicular height, so their volumes are equal.

Answer:

• The height of the cylinder is 3.4 ft.
• The diameter of the cylinder is about 3 ft.
• A right cylinder with the same height and radius as this oblique cylinder would also have a volume of $24 \text{ ft}^3$.