To find the base radius of a cone given its volume and height, we start with the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14
- [tex]\( r \)[/tex] is the base radius of the cone
- [tex]\( h \)[/tex] is the height of the cone
In this problem:
- [tex]\( V = 56.52 \, \text{in}^3 \)[/tex]
- [tex]\( h = 7 \, \text{in} \)[/tex]
- [tex]\( \pi \approx 3.14 \)[/tex]
We need to solve for [tex]\( r \)[/tex]. Rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r^2 = \frac{3V}{\pi h} \][/tex]
Substitute the given values into the equation:
[tex]\[ r^2 = \frac{3 \times 56.52}{3.14 \times 7} \][/tex]
First, calculate the numerator:
[tex]\[ 3 \times 56.52 = 169.56 \][/tex]
Next, calculate the denominator:
[tex]\[ 3.14 \times 7 = 21.98 \][/tex]
Now, divide the numerator by the denominator:
[tex]\[ r^2 = \frac{169.56}{21.98} \approx 7.714 \][/tex]
To find the radius, take the square root of both sides:
[tex]\[ r = \sqrt{7.714} \approx 2.7774602993176543 \][/tex]
Rounding to the tenths place:
[tex]\[ r \approx 2.8 \, \text{in} \][/tex]
Therefore, the best answer from the choices provided is:
[tex]\[ \text{b. 2.8 in} \][/tex]
