To find the radius of the cylinder given the volume and height, we can use the formula for the volume of a cylinder:
[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,
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159.
Given the volume [tex]\( V = 980 \)[/tex] cubic inches and the height [tex]\( h = 20 \)[/tex] inches, we need to solve for the radius [tex]\( r \)[/tex].
Step-by-step process:
1. Substitute the given values into the volume formula:
[tex]\[ 980 = \pi r^2 \times 20 \][/tex]
2. Rearrange the formula to solve for [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = \frac{980}{\pi \times 20} \][/tex]
3. Calculate the denominator [tex]\(\pi \times 20\)[/tex]:
[tex]\[ \pi \times 20 = 62.83185 \][/tex]
4. Divide the volume by this product to get [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = \frac{980}{62.83185} \approx 15.597025 \][/tex]
5. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{15.597025} \approx 3.949327084834294 \][/tex]
6. Round the radius to the nearest hundredth:
[tex]\[ r \approx 3.95 \][/tex]
Therefore, the radius of the cylinder, rounded to the nearest hundredth, is 3.95 inches.
So, the correct answer is:
a. 3.95 in.
