Question

find the volume of the solid figure.
image of a composite rectangular prism with dimensions: 10 yd, 12 yd, 11 yd, 5 yd, 7 yd, 3 yd, 7 yd

Explanation:

Step1: Split into two rectangular prisms

We can divide the solid into two separate rectangular prisms.
Prism 1 dimensions: length $10$ yd, width $5$ yd, height $11$ yd.
Prism 2 dimensions: length $12$ yd, width $3$ yd, height $11$ yd.

Step2: Calculate volume of Prism 1

Volume of a rectangular prism is $V = l \times w \times h$.
$V_1 = 10 \times 5 \times 11 = 550$ cubic yards

Step3: Calculate volume of Prism 2

Use the same volume formula for the second prism.
$V_2 = 12 \times 3 \times 11 = 396$ cubic yards

Step4: Sum the two volumes

Add the volumes of the two prisms to get total volume.
$V_{total} = V_1 + V_2 = 550 + 396$

Answer:

946 cubic yards