Question

give me a college math problem and solution

Answer 1

Certainly! Here’s a college-level math problem along with its solution:

### Problem:

A cylindrical tank has a radius of 3 meters and a height of 5 meters.

1. Calculate the volume of the tank.
2. If the tank is filled with water, how much does the water weigh? (Assume the density of water is \(1000 \, \text{kg/m}^3\).)

### Solution:

1. **Calculate the Volume of the Tank**

The formula for the volume \(V\) of a cylinder is given by:

\[
V = \pi r^2 h
\]

where:
- \(r\) is the radius,
- \(h\) is the height.

Given:
- \(r = 3 \, \text{m}\)
- \(h = 5 \, \text{m}\)

Plugging in the values:

\[
V = \pi (3)^2 (5)
\]
\[
V = \pi (9)(5)
\]
\[
V = 45\pi \, \text{m}^3
\]

Using \( \pi \approx 3.14 \):

\[
V \approx 45 \times 3.14 \approx 141.3 \, \text{m}^3
\]

### Volume of the tank is approximately \(141.3 \, \text{m}^3\).

2. **Calculate the Weight of the Water**

The weight \(W\) can be calculated using the formula:

\[
W = V \times \text{density}
\]

Given that the density of water is \(1000 \, \text{kg/m}^3\), we have:

\[
W = 141.3 \, \text{m}^3 \times 1000 \, \text{kg/m}^3
\]
\[
W = 141300 \, \text{kg}
\]

### The weight of the water in the tank is \(141300 \, \text{kg}\).

### Summary:

- Volume of the cylindrical tank: \(141.3 \, \text{m}^3\)
- Weight of the water when the tank is full: \(141300 \, \text{kg}\)