An illustration shows a 3 D pyramid with a rectangular base. The length, width, and height measurements are labeled. The sides on the front that are visible are shown as solid lines and the sides at the back are shown as dashed lines. The base length is labeled 10 centimeters and the width is labeled 7 centimeters. The height is shown as a dotted perpendicular line from the top vertex to the base and is labeled 11 centimeters. The dotted line continues to the base length to make a right angle.

Question

What is the volume of the pyramid?

Express your answer as a decimal rounded to the nearest hundredth.

Answer 1

To find the volume of a pyramid, we use the formula:

\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

First, we need to calculate the area of the rectangular base. The area of a rectangle can be found using the formula:

\[ \text{Base Area} = \text{length} \times \text{width} \]

Given:

• Length = 10 cm
• Width = 7 cm

Now, we calculate the base area:

\[ \text{Base Area} = 10 , \text{cm} \times 7 , \text{cm} = 70 , \text{cm}^2 \]

Next, we also have the height of the pyramid, which is given as 11 cm. Now, we can plug these values into the volume formula:

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

Calculating this step by step:

1. Calculate \(70 \times 11\):

\[ 70 \times 11 = 770 \]

2. Now apply the \(\frac{1}{3}\) factor:

\[ \text{Volume} = \frac{770}{3} \]

Calculating \(770 \div 3\):

\[ \frac{770}{3} \approx 256.6667 \]

So, rounding this to the nearest hundredth, we get:

\[ \text{Volume} \approx 256.67 , \text{cm}^3 \]

Thus, the volume of the pyramid is:

\[ \boxed{256.67} , \text{cm}^3 \]