To find the volume of a right circular cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius,
- [tex]\( h \)[/tex] is the height, and
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
Given:
- The radius [tex]\( r = 3 \)[/tex] inches,
- The height [tex]\( h = 10 \)[/tex] inches.
Let's substitute the given values into the formula.
First, we calculate the area of the base of the cylinder, which is a circle:
[tex]\[ r^2 = 3^2 = 9 \][/tex]
Next, we multiply this area by the height [tex]\( h \)[/tex]:
[tex]\[ 9 \times 10 = 90 \][/tex]
Now, we include the factor of [tex]\( \pi \)[/tex]:
[tex]\[ V = 90 \pi \][/tex]
So, the volume of the right circular cylinder is:
[tex]\[ 90 \pi \text{ cubic inches} \][/tex]
Given the options:
- [tex]\( 30 \pi \)[/tex] in[tex]\(^3\)[/tex]
- [tex]\( 60 \pi \)[/tex] in[tex]\(^3\)[/tex]
- [tex]\( 90 \pi \)[/tex] in[tex]\(^3\)[/tex]
- [tex]\( 120 \pi \)[/tex] in[tex]\(^3\)[/tex]
The correct answer is:
[tex]\[ 90 \pi \text{ cubic inches} \][/tex]
