To find the volume of a cone, we use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone,
- [tex]\( r \)[/tex] is the radius of the base of the cone,
- [tex]\( h \)[/tex] is the height of the cone,
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159.
Given:
- The radius [tex]\( r = 1.5 \)[/tex] inches,
- The height [tex]\( h = 6 \)[/tex] inches.
Plug these values into the formula:
[tex]\[ V = \frac{1}{3} \pi (1.5)^2 (6) \][/tex]
First, calculate the square of the radius:
[tex]\[ (1.5)^2 = 1.5 \times 1.5 = 2.25 \][/tex]
Next, multiply this result by the height:
[tex]\[ 2.25 \times 6 = 13.5 \][/tex]
Now, multiply by [tex]\( \pi \)[/tex]:
[tex]\[ \pi \times 13.5 \approx 3.14159 \times 13.5 \approx 42.4115 \][/tex]
Finally, divide by 3 to find the volume:
[tex]\[ V = \frac{42.4115}{3} \approx 14.13717 \][/tex]
To the nearest tenth of an inch, the volume is:
[tex]\[ V \approx 14.1 \][/tex]
Thus, the volume of the waffle cone is approximately [tex]\( 14.1 \ \text{in}^3 \)[/tex].
