Math Problem Statement

Find the volume of cubes with given side lengths and round the answers to two decimal places. Examples provided include side lengths of 1.7 in, 4.8 ft, and 6.4 yd, along with side lengths specified for calculation: 2.3 in, 7.2 yd, 5.1 ft, and 3.5 in.

Solution

This worksheet focuses on finding the volume of cubes using the formula:

Volume=side length3\text{Volume} = \text{side length}^3

I'll calculate the volume for each cube in both parts A and B as required. Let's break it down:


Part A: Find the volume of the cubes.

  1. Side length: 1.7 in
    Volume=1.73=4.913in3\text{Volume} = 1.7^3 = 4.913 \, \text{in}^3
    Rounded to two decimal places:
    Volume=4.91in3\text{Volume} = 4.91 \, \text{in}^3

  2. Side length: 4.8 ft
    Volume=4.83=110.592ft3\text{Volume} = 4.8^3 = 110.592 \, \text{ft}^3
    Rounded to two decimal places:
    Volume=110.59ft3\text{Volume} = 110.59 \, \text{ft}^3

  3. Side length: 6.4 yd
    Volume=6.43=262.144yd3\text{Volume} = 6.4^3 = 262.144 \, \text{yd}^3
    Rounded to two decimal places:
    Volume=262.14yd3\text{Volume} = 262.14 \, \text{yd}^3


Part B: Find the volume using the given side lengths.

  1. Side length: 2.3 in
    Volume=2.33=12.167in3\text{Volume} = 2.3^3 = 12.167 \, \text{in}^3
    Rounded to two decimal places:
    Volume=12.17in3\text{Volume} = 12.17 \, \text{in}^3

  2. Side length: 7.2 yd
    Volume=7.23=373.248yd3\text{Volume} = 7.2^3 = 373.248 \, \text{yd}^3
    Rounded to two decimal places:
    Volume=373.25yd3\text{Volume} = 373.25 \, \text{yd}^3

  3. Side length: 5.1 ft
    Volume=5.13=132.651ft3\text{Volume} = 5.1^3 = 132.651 \, \text{ft}^3
    Rounded to two decimal places:
    Volume=132.65ft3\text{Volume} = 132.65 \, \text{ft}^3

  4. Side length: 3.5 in
    Volume=3.53=42.875in3\text{Volume} = 3.5^3 = 42.875 \, \text{in}^3
    Rounded to two decimal places:
    Volume=42.88in3\text{Volume} = 42.88 \, \text{in}^3


Would you like detailed explanations for these calculations?

Here are some follow-up questions to expand your understanding:

  1. Why does the cube's volume formula involve cubing the side length?
  2. How would the calculations change if the side lengths were in different units (e.g., cm or meters)?
  3. Can you find the volume of a rectangular prism using a similar formula? How?
  4. What are some practical applications of calculating a cube's volume?
  5. How would rounding errors affect real-world applications of volume calculation?

Tip: Always double-check the units for side lengths and the resulting volume! Misinterpreted units can lead to incorrect results.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a Cube
Exponents

Formulas

Volume = side length^3

Theorems

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Suitable Grade Level

Grades 6-8