Finding the Remaining Volume of Consecutive Cubes

Finding the Remaining Volume of Consecutive Cubes

Assessment

Interactive Video

Mathematics, Information Technology (IT), Architecture

1st - 6th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

This video tutorial explains how to describe the relationship between the volumes of two consecutive cubes using polynomial identities. It covers the concept of consecutive integers, both regular and even/odd, and demonstrates how to simplify expressions to find the volume difference when a smaller cube is removed from a larger one. The tutorial also provides examples and step-by-step simplifications to illustrate these mathematical concepts.

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5 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a polynomial identity?

An equation that is true for some values of the variable

An equation that is true for all values of the variable

An equation that is true only for integers

An equation that is never true

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you represent the volume difference between two consecutive cubes?

x squared minus x plus 1 squared

x plus 1 cubed minus x cubed

x plus 2 cubed minus x cubed

x cubed minus x plus 1 cubed

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the volume difference when removing a cube with side length 3 from a larger cube with a consecutive integer side length?

27 cubic units

37 cubic units

57 cubic units

47 cubic units

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the polynomial identity change for consecutive even or odd integers?

It becomes x cubed minus x plus 2 cubed

It becomes x plus 1 cubed minus x cubed

It becomes x squared plus 2x plus 1

It becomes x plus 2 cubed minus x cubed

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified polynomial identity for consecutive even or odd integer cubes?

3x squared plus 3x plus 1

x cubed plus 3x squared plus 3x

6x squared plus 12x plus 8

x squared plus 4x plus 4

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