Question

a cone has a diameter of 8 cm and a height of 12 cm. what is its volume in terms of π?
a. 96π cm³
b. 64π cm³
c. 256π cm³
d. 48π cm³
when the radius of a cone is doubled, the volume of the cone:
a. is halved
b. is quadrupled
c. is doubled
d. remains the same

Explanation:

First Question:

Step1: Find the radius

The diameter \(d = 8\) cm, so the radius \(r=\frac{d}{2}=\frac{8}{2}=4\) cm.

Step2: Use the cone - volume formula

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(r = 4\) cm and \(h = 12\) cm.

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Second Question:

Step1: Recall the cone - volume formula

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\). Let the original radius be \(r\), so the original volume \(V_1=\frac{1}{3}\pi r^{2}h\).

Step2: Find the new volume when radius is doubled

When the radius is doubled (\(r_{new}=2r\)), the new volume \(V_2=\frac{1}{3}\pi(2r)^{2}h\).

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Answer:

For the first question: B. \(64\pi\space cm^{3}\)
For the second question: B. is quadrupled