Question
A container at the petting zoo holds 8138.88 cubic centimeters of grain. Visitors can fill paper cones with grain from the container. The cones have a radius of 4 centimeters and a height of 9 centimeters. How many times can you fill a cone with the grain that is stored in the container? Use 3.14 to approximate the value of pi
Answers
GPT-4o mini
To determine how many times we can fill a cone with grain from the container, we first need to calculate the volume of one cone. The formula for the volume of a cone is given by:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cone. Given that the radius \( r = 4 \) cm and the height \( h = 9 \) cm, we can substitute these values into the formula.
Using \( \pi \approx 3.14 \):
\[
V = \frac{1}{3} \times 3.14 \times (4^2) \times 9
\]
Calculating \( r^2 \):
\[
4^2 = 16
\]
Now substituting it back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 16 \times 9
\]
\[
= \frac{1}{3} \times 3.14 \times 144
\]
Calculating \( 3.14 \times 144 \):
\[
3.14 \times 144 = 452.16
\]
Now, we take one-third of that:
\[
V = \frac{452.16}{3} \approx 150.72 \text{ cubic centimeters}
\]
Now we know the volume of one cone is approximately 150.72 cubic centimeters.
Next, we calculate how many cones can be filled with the total volume of grain in the container, which is 8138.88 cubic centimeters:
\[
\text{Number of cones} = \frac{\text{Total volume of grain}}{\text{Volume of one cone}} = \frac{8138.88}{150.72}
\]
Calculating this value:
\[
\frac{8138.88}{150.72} \approx 53.96
\]
Since we can only fill whole cones, we take the floor of this number:
\[
\text{Number of cones} = 53
\]
Thus, the number of times we can fill a cone with the grain in the container is \( \boxed{53} \).
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cone. Given that the radius \( r = 4 \) cm and the height \( h = 9 \) cm, we can substitute these values into the formula.
Using \( \pi \approx 3.14 \):
\[
V = \frac{1}{3} \times 3.14 \times (4^2) \times 9
\]
Calculating \( r^2 \):
\[
4^2 = 16
\]
Now substituting it back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 16 \times 9
\]
\[
= \frac{1}{3} \times 3.14 \times 144
\]
Calculating \( 3.14 \times 144 \):
\[
3.14 \times 144 = 452.16
\]
Now, we take one-third of that:
\[
V = \frac{452.16}{3} \approx 150.72 \text{ cubic centimeters}
\]
Now we know the volume of one cone is approximately 150.72 cubic centimeters.
Next, we calculate how many cones can be filled with the total volume of grain in the container, which is 8138.88 cubic centimeters:
\[
\text{Number of cones} = \frac{\text{Total volume of grain}}{\text{Volume of one cone}} = \frac{8138.88}{150.72}
\]
Calculating this value:
\[
\frac{8138.88}{150.72} \approx 53.96
\]
Since we can only fill whole cones, we take the floor of this number:
\[
\text{Number of cones} = 53
\]
Thus, the number of times we can fill a cone with the grain in the container is \( \boxed{53} \).