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The volume of this cylinder is 1751 cubic units. What is the volume of a cone that has the same base area and the sam height

Sagot :

MrRoyal

Answer:

[tex]V_2 = 583.67[/tex]

Step-by-step explanation:

Given

Represent the volume of the cylinder with V1 and the cone with V2.

So:

[tex]V_1 = 1751[/tex]

Required

Find V2

The volume of a cylinder is:

[tex]V_1 = \pi r^2h[/tex]

Because the cone and the cylinder have the same base area and height, the volume of the cone is:

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

Substitute [tex]V_1[/tex] for [tex]\pi r^2h[/tex].

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

[tex]V_2 = \frac{1}{3}V_1[/tex]

Substitute 1751 for V1

[tex]V_2 = \frac{1}{3} * 1751[/tex]

[tex]V_2 = \frac{1* 1751}{3}[/tex]

[tex]V_2 = \frac{1751}{3}[/tex]

[tex]V_2 = 583.67[/tex]

The volume of the cone is 583.67 cubic units

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