Math Problem Statement

What is the volume of a rectangular prism with dimensions 3 cm, 8 cm, and 19 cm?

Solution

To find the volume of the rectangular prism in the image, we use the formula:

Volume=length×width×height\text{Volume} = \text{length} \times \text{width} \times \text{height}

Given dimensions:

  • Length = 8 cm
  • Width = 3 cm
  • Height = 19 cm

Plugging these values into the formula:

Volume=8cm×3cm×19cm=456cubic centimeters\text{Volume} = 8 \, \text{cm} \times 3 \, \text{cm} \times 19 \, \text{cm} = 456 \, \text{cubic centimeters}

Answer:

The volume is 456 cubic centimeters.

Would you like more details or have any questions?


Here are 5 related questions to deepen understanding:

  1. How would the volume change if the height were doubled?
  2. What is the formula for finding the surface area of this rectangular prism?
  3. If only the width were doubled, what would the new volume be?
  4. How do units affect volume calculations in different measurements (e.g., cm³ vs. m³)?
  5. How does the concept of volume apply to different shapes like cylinders or spheres?

Tip: Remember that the units for volume are always in cubic units, such as cubic centimeters (cm³), because volume measures three-dimensional space.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume Calculation
Rectangular Prisms

Formulas

Volume = length × width × height

Theorems

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Suitable Grade Level

Grades 5-7