To determine how much ice cream can be put into a cone with a height of 12 cm and a base radius of 3.5 cm, we need to calculate the volume of the cone. The volume [tex]\( V \)[/tex] of a cone can be found using the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone
- [tex]\( r \)[/tex] is the radius of the base
- [tex]\( h \)[/tex] is the height of the cone
- [tex]\( \pi \)[/tex] is the constant Pi (approximately 3.14159)
Given:
- Height, [tex]\( h \)[/tex] = 12 cm
- Radius, [tex]\( r \)[/tex] = 3.5 cm
Now, we substitute the given values into the formula:
1. Calculate the square of the radius:
[tex]\[ r^2 = 3.5^2 = 12.25 \][/tex]
2. Multiply this by the height of the cone:
[tex]\[ 12.25 \times 12 = 147 \][/tex]
3. Multiply by [tex]\(\pi\)[/tex] (approximately 3.14159):
[tex]\[ \pi \times 147 \approx 3.14159 \times 147 = 461.81283 \][/tex]
4. Finally, multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{3} \times 461.81283 \approx 153.93804002589985 \][/tex]
Therefore, the volume of the cone, which represents how much ice cream can be put into it, is approximately:
[tex]\[ 153.94 \, \text{cm}^3 \][/tex]
So, about 153.94 cubic centimeters of ice cream can be put into the cone.
