a Caution wet floor warning sign is in the shape of a rectangular pyramid. It is 31 in tall and has a base whose dimensions are 12 in by 20 in. What is the volume of the sign

Answer 1

To find the volume of a rectangular pyramid, you can use the formula:

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

1. First, calculate the area of the base. The base dimensions are 12 inches by 20 inches:

\[ \text{Base Area} = \text{Length} \times \text{Width} = 12 , \text{in} \times 20 , \text{in} = 240 , \text{in}^2 \]

2. The height of the pyramid is given as 31 inches.

3. Now, plug the values into the volume formula:

\[ V = \frac{1}{3} \times 240 , \text{in}^2 \times 31 , \text{in} \]

4. Calculate the volume:

\[ V = \frac{1}{3} \times 240 \times 31 \]

5. First, compute \( 240 \times 31 \):

\[ 240 \times 31 = 7440 \]

6. Now divide by 3:

\[ V = \frac{7440}{3} = 2480 , \text{in}^3 \]

Therefore, the volume of the rectangular pyramid warning sign is 2480 cubic inches.