To calculate the volume of the cylindrical cake mold, we need to use the formula for the volume of a cylinder:
[tex]\[ V = \pi r^2 h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume.
- [tex]\( \pi \)[/tex] is the constant pi (approximated here as [tex]\(\pi = \frac{355}{113}\)[/tex]).
- [tex]\( r \)[/tex] is the radius of the cylinder's base.
- [tex]\( h \)[/tex] is the height of the cylinder.
Given:
- Diameter of the cylinder [tex]\(d = 8 \text{ inches}\)[/tex].
- Height of the cylinder [tex]\(h = 6 \text{ inches}\)[/tex].
First, find the radius [tex]\( r \)[/tex]:
[tex]\[ r = \frac{d}{2} = \frac{8}{2} = 4 \text{ inches} \][/tex]
Now substitute the values into the volume formula:
[tex]\[ V = \left( \frac{355}{113} \right) \times 4^2 \times 6 \][/tex]
Calculate [tex]\(4^2\)[/tex]:
[tex]\[ 4^2 = 16 \][/tex]
So the expression becomes:
[tex]\[ V = \left( \frac{355}{113} \right) \times 16 \times 6 \][/tex]
Now perform the multiplication:
[tex]\[ 16 \times 6 = 96 \][/tex]
Therefore, the volume calculation simplifies to:
[tex]\[ V = \left( \frac{355}{113} \right) \times 96 \][/tex]
Upon evaluating this expression (knowing the precise result from running the actual calculation), we get:
[tex]\[ V \approx 301.59 \text{ cubic inches} \][/tex]
So, the correct method to calculate the number of cubic units of cake batter needed to fill the mold is:
[tex]\[ V = \left(\frac{355}{113}\right) (4)^2 (6) \][/tex]
