Question
A spherical tank has a radius of 6 yards. It is filled with a liquid that costs $7.15 per cubic yard.
What is the total value of the liquid in the tank?
Use 3.14 for n.
Enter your answer in the box to the nearest cent.
$
What is the total value of the liquid in the tank?
Use 3.14 for n.
Enter your answer in the box to the nearest cent.
$
Answers
GPT-4o mini
To find the total value of the liquid in a spherical tank, we first need to calculate the volume of the sphere using the formula for the volume of a sphere:
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius of the sphere. Given that the radius \( r \) is 6 yards and using \( \pi \approx 3.14 \), we can calculate the volume as follows:
\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]
First, we calculate \( (6)^3 \):
\[
(6)^3 = 6 \times 6 \times 6 = 216
\]
Next, we can substitute this back into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Calculating \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867 \quad \text{(approximately)}
\]
Now, we multiply by 216:
\[
V \approx 4.1867 \times 216
\]
Calculating that gives:
\[
V \approx 904.0 \quad \text{(approximately)}
\]
Now we can find the value of the liquid in the tank by multiplying the volume by the cost per cubic yard:
\[
\text{Value} = V \times \text{cost per cubic yard} = 904.0 \times 7.15
\]
Calculating that:
\[
\text{Value} \approx 904.0 \times 7.15 \approx 6456.60
\]
Thus, the total value of the liquid in the tank, rounded to the nearest cent, is:
\[
\boxed{6456.60}
\]
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius of the sphere. Given that the radius \( r \) is 6 yards and using \( \pi \approx 3.14 \), we can calculate the volume as follows:
\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]
First, we calculate \( (6)^3 \):
\[
(6)^3 = 6 \times 6 \times 6 = 216
\]
Next, we can substitute this back into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Calculating \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867 \quad \text{(approximately)}
\]
Now, we multiply by 216:
\[
V \approx 4.1867 \times 216
\]
Calculating that gives:
\[
V \approx 904.0 \quad \text{(approximately)}
\]
Now we can find the value of the liquid in the tank by multiplying the volume by the cost per cubic yard:
\[
\text{Value} = V \times \text{cost per cubic yard} = 904.0 \times 7.15
\]
Calculating that:
\[
\text{Value} \approx 904.0 \times 7.15 \approx 6456.60
\]
Thus, the total value of the liquid in the tank, rounded to the nearest cent, is:
\[
\boxed{6456.60}
\]