Question

In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be StartFraction pi Over 4 EndFraction times the volume of the pyramid that it fits inside. A cone is inside of a pyramid with a square base. The cone has a radius of r and a height of h. The length of the base edge of the pyramid is 2 r. Which expression represents the volume of the cone that is StartFraction pi Over 4 EndFraction times the volume of the pyramid that it fits inside? StartFraction pi Over 4 EndFraction(2r2h) StartFraction pi Over 4 EndFraction(4r2h) StartFraction pi Over 4 EndFraction(StartFraction r squared h Over 3 EndFraction) StartFraction pi Over 4 EndFraction(StartFraction 4 r squared h Over 3 EndFraction).

Answer 1

The volume of a cone is the amount of space in the cone

The expression that represents the volume of the cone is: $\frac{\pi}{4} \cdot \frac{4r^2h}{3}$

How to determine the volume of the cone

The equation is given as:

$V_c =\frac{\pi}{4} * V_p$

Where:

• Vc represents the volume of the cone
• Vp represents the volume of the pyramid that fits inside the cone

From the diagram, the volume of the pyramid is:

$V_p = \frac{4r^2h}{3}$

Substitute the above value for Vp in the equation that represents the volume of a cone.

So, we have:

$V_c = \frac{\pi}{4} \cdot \frac{4r^2h}{3}$

Hence, the expression that represents the volume of the cone is: $\frac{\pi}{4} \cdot \frac{4r^2h}{3}$

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