Calculating Pond Capacity from Dimensions

This problem asks us to find the capacity of a pond given its three dimensions: length, width, and depth. The capacity of an object like a pond typically refers to its volume, which is the amount of space it occupies or can hold.

Pond Dimensions Analysis

The given dimensions of the pond are:

• Length ($l$): 20 m
• Width ($w$): 14 m
• Depth ($h$): 6 m

Since the pond has three distinct dimensions (length, width, depth), we can model it as a rectangular prism (or cuboid). The volume of a rectangular prism represents its capacity.

Capacity Calculation Steps

To find the capacity (volume) of the pond, we use the formula for the volume of a rectangular prism:

$$ V = l \times w \times h $$

Where:

• $V$ is the volume (capacity)
• $l$ is the length
• $w$ is the width
• $h$ is the height (or depth in this case)

Now, let's substitute the given dimensions into the formula:

$$ V = 20 \, \text{m} \times 14 \, \text{m} \times 6 \, \text{m} $$

First, multiply the length and width:

$$ 20 \times 14 = 280 $$

So, the area of the base is 280 square meters ($m^2$).

Next, multiply this area by the depth:

$$ V = 280 \, m^2 \times 6 \, \text{m} $$

$$ V = 1680 \, m^3 $$

The calculation shows that the volume of the pond is 1680 cubic meters ($m^3$). This represents the pond's capacity.

Final Answer Check

Comparing our calculated capacity with the given options:

• 1460 $m^3$
• 1520 $m^3$
• 1680 $m^3$
• 1280 $m^3$

Our calculated volume, 1680 $m^3$, matches the third option.