Question

17,524 Learners found this answer helpful

the figure is composed of a rectangular prism and a triangular prism. find the volume of the figure. the volume of the figure is \boxed{} in.³.

Explanation:

Step1: Volume of Rectangular Prism

The formula for the volume of a rectangular prism is \( V_{rect} = l \times w \times h \). Here, \( l = 29 \) in, \( w = 14 \) in, \( h = 14 \) in. So, \( V_{rect} = 29 \times 14 \times 14 \).
\[
V_{rect} = 29 \times 196 = 5684
\]

Step2: Volume of Triangular Prism

The formula for the volume of a triangular prism is \( V_{tri} = \frac{1}{2} \times b \times h \times l \). Here, the base of the triangle \( b = 14 \) in, height of the triangle \( h = 7 \) in, and length \( l = 29 \) in. So, \( V_{tri} = \frac{1}{2} \times 14 \times 7 \times 29 \).
\[
V_{tri} = 7 \times 7 \times 29 = 49 \times 29 = 1421
\]

Step3: Total Volume

Add the volumes of the two prisms: \( V_{total} = V_{rect} + V_{tri} \).
\[
V_{total} = 5684 + 1421 = 7105
\]

Answer:

7105