To find the volume of a right circular cone with a given height and radius, we use the formula for the volume of a cone, which is:
[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] (pi) is a constant approximately equal to 3.14159.
Given:
- The height [tex]\( h = 7.2 \)[/tex] centimeters,
- The radius [tex]\( r = 2.5 \)[/tex] centimeters.
Let's substitute the given values into the formula:
[tex]\[ V = \frac{1}{3} \pi (2.5)^2 (7.2) \][/tex]
First, calculate the square of the radius:
[tex]\[ (2.5)^2 = 6.25 \][/tex]
Now substitute this back into the formula:
[tex]\[ V = \frac{1}{3} \pi (6.25) (7.2) \][/tex]
Next, multiply 6.25 and 7.2:
[tex]\[ 6.25 \times 7.2 = 45 \][/tex]
Now our equation looks like this:
[tex]\[ V = \frac{1}{3} \pi (45) \][/tex]
Multiply 45 by [tex]\(\pi\)[/tex]:
[tex]\[ \pi (45) \approx 141.3716694115407 \][/tex]
Now, divide by 3 to get the volume:
[tex]\[ V = \frac{141.3716694115407}{3} \approx 47.1238898038469 \][/tex]
The volume calculated is approximately 47.1238898038469 cubic centimeters.
To express this volume to the nearest tenth, we round 47.1238898038469 to one decimal place:
[tex]\[ V \approx 47.1 \][/tex]
Therefore, the volume of the right circular cone, to the nearest tenth of a cubic centimeter, is:
[tex]\[ 47.1 \][/tex]
So, the final answer is 47.1 cubic centimeters.
