Question

What is the volume of the pyramid? The pyramid is 11cm tall, 7 cm long, 10 cm wide

Answer 1

The volume \( V \) of a pyramid can be calculated using the formula:

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

For a rectangular base, the area is given by:

\[
\text{base area} = \text{length} \times \text{width}
\]

In this case, the pyramid has the following dimensions:
- Height \( h = 11 \) cm
- Length \( l = 7 \) cm
- Width \( w = 10 \) cm

First, calculate the base area:

\[
\text{base area} = l \times w = 7 \, \text{cm} \times 10 \, \text{cm} = 70 \, \text{cm}^2
\]

Now, use the base area to calculate the volume:

\[
V = \frac{1}{3} \times 70 \, \text{cm}^2 \times 11 \, \text{cm}
\]

\[
V = \frac{1}{3} \times 770 \, \text{cm}^3
\]

\[
V = \frac{770}{3} \, \text{cm}^3 \approx 256.67 \, \text{cm}^3
\]

Thus, the volume of the pyramid is approximately \( 256.67 \, \text{cm}^3 \).