If a cone has a radius of 3 cm and height of 4 cm, what is the volume?

To find the volume of a cone, you can use the formula:

[

V = \frac{1}{3} \pi r^2 h

]

where ( V ) is the volume, ( r ) is the radius of the base, and ( h ) is the height of the cone.

For this cone, the radius ( r ) is 3 cm and the height ( h ) is 4 cm. Plugging these values into the formula gives:

1. Calculate ( r^2 ):

[

r^2 = 3^2 = 9

]

2. Now substitute ( r^2 ) and ( h ) into the formula:

[

V = \frac{1}{3} \pi (9) (4)

]

3. Multiply the values:

[

V = \frac{1}{3} \pi (36)

]

4. Finally, simplify:

[

V = 12\pi \text{ cm}^3

]

This means the volume of the cone is ( 12\pi ) cm³, which aligns with the choice