Question

leslie found the volume of a cone having both a height and diameter of 12 inches. leslies work 1. radius = \\( \frac { 1 2 } { 2 } = 6 \\) in. 2. base area = \\( \pi 6 ^ { 2 } = 3 6 \pi \\) in² 3. cone volume = \\( 3 6 \pi ( 1 2 ) = 4 3 2 \pi \\) in³ analyze leslies work. is she correct? if not, what was her mistake? yes, she is correct. no, the value of \\( 6 ^ { 2 } \\) is 6 times 2, or 12. no, the radius is twice the diameter, so she needed to multiply by two instead of dividing. no, she forgot to take one - third of the base area times height.

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \(V=\frac{1}{3}Bh\) (where \(B\) is the base area and \(h\) is the height).

Step2: Analyze Leslie's work

Leslie calculated \(V = Bh\) (she did \(36\pi\times12\)) instead of \(V=\frac{1}{3}Bh\).

Answer:

No, she forgot to take one - third of the base area times height.