Respuesta :
The correct statements about the volume of the cone are:
- The volume of the cone is One-third the volume of the cylinder.
- The expression 84 pi over 3 finds the volume of the cone.
- The volume of the cone is less than the volume of the cylinder.
What is the volume of cylinder?
[tex]V=\pi\times r^2\times h[/tex]
where 'r' is the radius of the base of the cylinder and 'h' is height of the cylinder
What is the volume of the cone?
[tex]V=\pi\times r^2\times \frac{h}{3}[/tex]
where 'r' is the radius of the base of the cone and 'h' is height of the cone
For given example,
The volume of the cylinder is 84 pi inches cubed.
Let [tex]V_1[/tex] represents the volume of the cylinder.
[tex]V_1=84~~cu.in.[/tex]
Using the formula of the volume of the cylinder,
[tex]V_1=\pi\times r^2\times h[/tex]
where 'r' is the radius of the base of the cylinder and 'h' is height of the cylinder
Let [tex]V_2[/tex] be the volume of the cone.
Assume that the base radius 'r' and height 'h' of the cone and the cylinder are equal.
Using the formula of the volume of the cone,
[tex]\Rightarrow V_2=\pi\times r^2\times \frac{h}{3}\\\\\Rightarrow V_2=\frac{1}{3}\times( \pi\times r^2\times h) \\\\\Rightarrow V_2=\frac{1}{3}\times V_1[/tex]
This means, the volume of the cone is One-third the volume of the cylinder.
[tex]\Rightarrow V2=\frac{1}{3}\times 84[/tex]
This means, the expression 84 pi over 3 finds the volume of the cone.
[tex]\Rightarrow V_2=28~~cu.in.\pi \\\\\Rightarrow V_2 < V_1[/tex]
This means, the volume of the cone is less than the volume of the cylinder.
Therefore, the correct statements about the volume of the cone are:
- The volume of the cone is One-third the volume of the cylinder.
- The expression 84 pi over 3 finds the volume of the cone.
- The volume of the cone is less than the volume of the cylinder.
Learn more about the volume of the cylinder and the volume of the cone here:
https://brainly.com/question/16007458
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