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).

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MrRoyal MrRoyal · Answer 1 · 2022-02-01T11:43:56+01:00

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

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

The equation is given as:

[tex]V_c =\frac{\pi}{4} * V_p[/tex]

Where:

From the diagram, the volume of the pyramid is:

[tex]V_p = \frac{4r^2h}{3}[/tex]

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

So, we have:

[tex]V_c = \frac{\pi}{4} \cdot \frac{4r^2h}{3}[/tex]

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