To determine the volume of the cylindrical jar, we need to use the formula for the volume of a cylinder. The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14
- [tex]\( r \)[/tex] is the radius of the base of the cylinder
- [tex]\( h \)[/tex] is the height of the cylinder
First, we need to find the radius [tex]\( r \)[/tex] of the cylinder. The radius is half of the diameter. Given the diameter of the cylinder is 4 inches, the radius [tex]\( r \)[/tex] can be calculated as:
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{4 \text{ inches}}{2} = 2 \text{ inches} \][/tex]
Now we can substitute the values for [tex]\( \pi \)[/tex], [tex]\( r \)[/tex], and [tex]\( h \)[/tex] into the volume formula. We are given:
- [tex]\( \pi = 3.14 \)[/tex]
- [tex]\( r = 2 \)[/tex] inches
- [tex]\( h = 5 \)[/tex] inches
Substituting these values into the formula:
[tex]\[ V = 3.14 \times (2 \text{ inches})^2 \times 5 \text{ inches} \][/tex]
Calculating the square of the radius:
[tex]\[ (2 \text{ inches})^2 = 4 \text{ square inches} \][/tex]
Now multiplying:
[tex]\[ V = 3.14 \times 4 \text{ square inches} \times 5 \text{ inches} \][/tex]
[tex]\[ V = 3.14 \times 20 \text{ cubic inches} \][/tex]
[tex]\[ V = 62.8 \text{ cubic inches} \][/tex]
Therefore, the volume of the cylindrical jar is:
[tex]\[ 62.8 \text{ cubic inches} \][/tex]
So, the correct answer is:
[tex]\[ 62.8 \text{ in}^3 \][/tex]
