Volume Word Problems
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Examples, solutions, videos, worksheets, games, and activities to help Algebra students learn how to solve word problems that involve the volume of an open box or a rectangular prism.
Algebra word problems involving volume require setting up and solving equations based on the formulas for the volume of 3D shapes. These problems often involve finding unknown dimensions or volumes using algebraic methods.
Here are some examples of algebra word problems involving volume, along with step-by-step solutions.
The following diagram gives the steps to solve volume word problem using Algebra.
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How to find the dimensions of a cardboard used to form a box given the volume of the box?
Example:
The length of a piece of cardboard is five inches more than the width. The four corners are cut off so that the sides can be folded up to form a box. Each of the cut corners measures one and a half inches by one and a half inches, and the volume of the box is 189 cubic inches. What are the original dimensions of the piece of cardboard?
Volume Word Problems - Geometry Help
Open box volume problem
Example:
An open box with a square base is to be made from a square piece of cardboard 36 inches on a side by cutting out a square from each corner and turning up the sides.
(a) Express the volume V of the box as a function of the length of the side of the square cut from each corner.
(b) What is the volume if a 7-inch square is cut out?
(c) What is the volume if a 16-inch square is cut out?
(d) Graph V(x). Choose the correct graph.
Find width and length of open box given the volume
Example:
A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 3354 in3, what were the original dimensions of the piece of metal?
Volume of an Open Box
This video will demonstrate how to calculate the maximum volume of an open box when congruent squares are removed from a rectangular sheet of cardboard. (We will use a graphing calculator and will not be using calculus)
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