Question

which statements about the cone are true? choose four correct answers. the volume is one - third the volume of a cylinder with the same height and diameter. the volume of the cone is 297π mm³. the radius is 9 mm. the base area is calculated using the radius. the radius is double the diameter.

Explanation:

Step1: Recall the relationship between cone and cylinder volume

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\), and the volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). So, the volume of a cone is one - third the volume of a cylinder with the same height and radius (or diameter, since diameter \(d = 2r\)).

Step2: Calculate the radius

Given the diameter \(d=18\) mm. Using the formula \(r=\frac{d}{2}\), we have \(r = \frac{18}{2}=9\) mm.

Step3: Calculate the base area

The base area of a cone (which is a circle) is \(A=\pi r^{2}\), so it is calculated using the radius.

Step4: Calculate the volume of the cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(r = 9\) mm and \(h=11\) mm into the formula:

$$
LATEXBLOCK0
$$

Step5: Analyze the radius - diameter relationship

The formula relating radius and diameter is \(d = 2r\), not \(r = 2d\). So the statement "The radius is double the diameter" is false.

Answer:

• The volume is one - third the volume of a cylinder with the same height and diameter.
• The radius is 9 mm.
• The base area is calculated using the radius.
• The volume of the cone is \(297\pi\space mm^{3}\).