Step 1: Understanding the Concept:
This question is based on the volume of a three-dimensional solid, specifically a cylinder.
The volume of a cylinder represents the total capacity of the tank and depends on the base area and the vertical height.
Step 2: Key Formula or Approach:
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
Where:
\( r \) = radius of the cylinder.
\( h \) = height of the cylinder.
\( \pi \approx \frac{22}{7} \).
Step 3: Detailed Explanation:
We are given the following values in the problem:
Radius \( r = 7\text{ m} \)
Height \( h = 10\text{ m} \)
Now, substitute these values into the volume formula:
\[ V = \frac{22}{7} \times (7)^2 \times 10 \]
Calculate the square of the radius first:
\[ 7^2 = 49 \]
The expression becomes:
\[ V = \frac{22}{7} \times 49 \times 10 \]
Cancel out the common factor of 7 from the denominator and 49:
\[ V = 22 \times 7 \times 10 \]
First, multiply 22 by 7:
\[ 22 \times 7 = 154 \]
Then, multiply by the height:
\[ 154 \times 10 = 1540 \]
Since the dimensions are in meters, the volume will be in cubic meters.
Step 4: Final Answer:
The volume of the water tank is $1540\text{ m}^3$.