Math Problem Statement

Determine the volume of the composite figure with dimensions as shown: a bottom rectangular prism with 8 in height, 5 in width, and 5 in depth, and a top rectangular prism with 7 in height, 5 in width, and 1 in depth.

Solution

To determine the volume of the given figure, we can divide it into two separate rectangular prisms and then find the volume of each prism individually.

  1. Bottom rectangular prism:

    • Dimensions: 8 in (height) × 5 in (width) × 5 in (depth)
    • Volume = 8×5×5=2008 \times 5 \times 5 = 200 cubic inches
  2. Top rectangular prism:

    • Dimensions: 7 in (height) × 5 in (width) × 1 in (depth)
    • Volume = 7×5×1=357 \times 5 \times 1 = 35 cubic inches
  3. Total volume of the figure:

    • Volume = 200+35=235200 + 35 = 235 cubic inches

So, the total volume of the figure is 235 cubic inches.

Would you like more details on the steps or have any other questions?

Related Questions:

  1. How do you find the volume of composite figures?
  2. Can you show the difference between volume and surface area?
  3. How do you calculate the volume of a prism with different shapes?
  4. What is the formula for the volume of a cylinder?
  5. How do you convert volume units from cubic inches to cubic centimeters?

Tip:

When dealing with composite figures, it's often helpful to break them down into simpler shapes, find the volume of each part, and then add or subtract them as needed.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Volume of Prisms
Composite Shapes

Formulas

Volume of a rectangular prism = length × width × height

Theorems

-

Suitable Grade Level

Grades 6-8