QQuestionMathematics
QuestionMathematics
What is the volume of this rectangular pyramid?
13 in
13 in
15 in
cubic inches
about 1 year agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the base dimensions and height of the rectangular pyramid.
The base of the pyramid is a rectangle, and its side lengths are given as 13 in. Each. The height of the pyramid is 15 in.
Step 2:: Write down the formula for the volume of a rectangular pyramid.
V = \frac{1}{3} \times \text{base area} \times \text{height}
The volume V of a rectangular pyramid is given by the formula:
Step 3:: Calculate the base area.
A = 13 \text{ in} \times 13 \text{ in} = 169 \text{ in}^2
The base area of this pyramid is a rectangle with side lengths 13 in. Each. The area A of a rectangle is given by the formula: So,
Step 4:: Substitute the base area and height into the volume formula.
V = \frac{1}{3} \times 169 \text{ in}^2 \times 15 \text{ in}
Now, we can find the volume V of the pyramid by substituting the base area A and the height h into the volume formula:
Step 5:: Calculate the final volume.
V = \frac{1}{3} \times 169 \text{ in}^2 \times 15 \text{ in} = \boxed{845 \text{ in}^3}
Finally, we can calculate the volume V of the rectangular pyramid:
Final Answer
The volume of the rectangular pyramid is 845 cubic inches.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students