Question

question 10
a cone and a cylinder have the same height and the same radius. explain how their volumes compare. then, if the cylinder has a volume of 150 cm³, what is the volume of the cone? show how you know.
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Explanation:

Step1: Recall volume formulas

The volume formula for a cylinder is \( V_{cylinder}=\pi r^{2}h \), and for a cone is \( V_{cone}=\frac{1}{3}\pi r^{2}h \). Since \( r \) (radius) and \( h \) (height) are the same for both, the volume of the cone is \(\frac{1}{3}\) of the volume of the cylinder.

Step2: Calculate the cone's volume

Given \( V_{cylinder} = 150\ cm^{3} \). Using the relationship \( V_{cone}=\frac{1}{3}V_{cylinder} \), substitute \( V_{cylinder} \): \( V_{cone}=\frac{1}{3}\times150 \).

Answer:

The volume of the cone is \( 50\ cm^{3} \) because the volume of a cone with the same radius and height as a cylinder is one - third of the cylinder's volume. Mathematically, \( V_{cone}=\frac{1}{3}\times150 = 50\ cm^{3} \).