Question
A paper cup in the shape of an inverted cone is 8 inches tall and has a radius of 1.5 inches. How much water can the cup hold? Use 3.14 for Pi. Round the answer to the nearest tenth.
12.6 cubic in.
18.8 cubic in.
37.7 cubic in.
56.5 cubic in.
12.6 cubic in.
18.8 cubic in.
37.7 cubic in.
56.5 cubic in.
Answers
GPT-4o mini
To find the volume of a cone, the formula is:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( \pi \) is a constant (you provided 3.14), \( r \) is the radius, and \( h \) is the height.
In this case, the radius \( r = 1.5 \) inches and the height \( h = 8 \) inches. Plugging in these values:
\[
V = \frac{1}{3} \times 3.14 \times (1.5)^2 \times 8
\]
First, calculate \( (1.5)^2 \):
\[
(1.5)^2 = 2.25
\]
Next, substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 2.25 \times 8
\]
Now calculate \( 3.14 \times 2.25 \):
\[
3.14 \times 2.25 = 7.065
\]
Now multiply by 8:
\[
7.065 \times 8 = 56.52
\]
Finally, multiply by \( \frac{1}{3} \):
\[
V = \frac{56.52}{3} \approx 18.84
\]
Rounding to the nearest tenth, the volume of the cup is approximately \( 18.8 \) cubic inches.
Thus, the answer is:
**18.8 cubic in.**
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( \pi \) is a constant (you provided 3.14), \( r \) is the radius, and \( h \) is the height.
In this case, the radius \( r = 1.5 \) inches and the height \( h = 8 \) inches. Plugging in these values:
\[
V = \frac{1}{3} \times 3.14 \times (1.5)^2 \times 8
\]
First, calculate \( (1.5)^2 \):
\[
(1.5)^2 = 2.25
\]
Next, substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 2.25 \times 8
\]
Now calculate \( 3.14 \times 2.25 \):
\[
3.14 \times 2.25 = 7.065
\]
Now multiply by 8:
\[
7.065 \times 8 = 56.52
\]
Finally, multiply by \( \frac{1}{3} \):
\[
V = \frac{56.52}{3} \approx 18.84
\]
Rounding to the nearest tenth, the volume of the cup is approximately \( 18.8 \) cubic inches.
Thus, the answer is:
**18.8 cubic in.**