Question

A hemispherical tank is filled with water and has a diameter of 20 feet. If water weighs 64.4 pounds per cubic foot, what is the total mass of the water in a full tank to the nearest pound?

Question 2 options:

1,079,032 lbs


269,758 lbs


134,879 lbs


67,939 lbs

Answer 1

To find the mass of the water in a full hemispherical tank, we need to follow these steps:

1. **Calculate the volume of the hemisphere**:
The formula for the volume \( V \) of a hemisphere is given by:
\[
V = \frac{2}{3} \pi r^3
\]
where \( r \) is the radius.

Given the diameter of the tank is 20 feet, the radius \( r \) is half of the diameter:
\[
r = \frac{20}{2} = 10 \text{ feet}
\]

Now, substituting \( r = 10 \) feet into the volume formula:
\[
V = \frac{2}{3} \pi (10)^3 = \frac{2}{3} \pi (1000) = \frac{2000}{3} \pi
\]

2. **Calculate the volume**:
Using \( \pi \approx 3.14159 \):
\[
V \approx \frac{2000}{3} \times 3.14159 \approx \frac{2000 \times 3.14159}{3} \approx \frac{6283.18}{3} \approx 2094.26 \text{ cubic feet}
\]

3. **Calculate the mass of the water**:
The mass \( m \) of the water can be calculated by multiplying the volume by the weight density of water:
\[
m = V \times \text{density}
\]
Given that the density of water is 64.4 pounds per cubic foot, we have:
\[
m \approx 2094.26 \times 64.4
\]
\[
m \approx 134,871.78 \text{ pounds}
\]

4. **Round to the nearest pound**:
Thus, rounding \( 134,871.78 \) to the nearest pound, we get:
\[
m \approx 134,872 \text{ pounds}
\]
However, since this value does not match any of the provided options exactly, we consider the option closest to our calculated mass.

Among the provided options:
- 1,079,032 lbs
- 269,758 lbs
- 134,879 lbs
- 67,939 lbs

The closest answer to our calculated mass of \( 134,872 \) pounds is **134,879 lbs**.

Thus, the answer is:
**134,879 lbs**.