If the height of the pyramid is 14, what is its volume?

Understand the Problem

The question is asking us to calculate the volume of a pyramid given its height (14) and the dimensions of its base (3 and 15). The formula for the volume of a pyramid is V = (1/3) * base area * height.

Answer

The volume of the pyramid is $210$.

Steps to Solve

Calculate the area of the base

The base of the pyramid is a rectangle. To find the area of the rectangle, we use the formula:

$$ \text{Area} = \text{length} \times \text{width} $$

Substituting the given dimensions:

$$ \text{Area} = 15 \times 3 = 45 $$

Apply the volume formula

Now that we have the area of the base, we can use the formula for the volume of a pyramid:

$$ V = \frac{1}{3} \times \text{base area} \times \text{height} $$

Substituting in the values we calculated:

$$ V = \frac{1}{3} \times 45 \times 14 $$

Calculate the volume

First, calculate ( 45 \times 14 ):

$$ 45 \times 14 = 630 $$

Then, divide by 3:

$$ V = \frac{630}{3} = 210 $$

The volume of the pyramid is $210$.

More Information

The volume of a pyramid can be calculated using the base area and height. In this case, the base is a rectangle, and by aligning dimensions properly, we derived the pyramid's volume effectively.

Tips

Forgetting to calculate the area of the base correctly.
Incorrectly substituting values into the volume formula, especially with height and area.
Miscalculating the final volume by failing to divide correctly.

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