Answer:
a
Step-by-step explanation:
To find the volume of a cone, you can use the formula:
[tex]V=\frac{1}{3} \pi r^2h[/tex]
Where:
V is the volume
[tex]\pi[/tex] is a constant approximately equal to 3.14159
r is the radius of the base of the cone
h is the height of the cone
Given that the area of the base of the cone is 12, we need to find the radius (r) first.
The formula for the area of the base of a cone is:
[tex]A = \pi r^2[/tex]
Given A = 12, we can rearrange the formula to solve for r:
[tex]12 = \pi r^2\\\\r^2 = \frac{12}{\pi}\\\\r = \sqrt{\frac{12}{\pi}}[/tex]
Now, we can plug the values of r and h into the volume formula:
[tex]V = \frac{1}{3} \pi \left(\sqrt{\frac{12}{\pi}}\right)^2 \times 6\\\\V = \frac{1}{3} \pi \times \frac{12}{\pi} \times 6\\\\V = \frac{1}{3} \times 12 \times 6\\\\V = 24[/tex]