Math Problem Statement
Solution
Let's go through the questions in the image and solve them step by step.
Question 15:
The problem asks to write expressions for liters in different units, knowing that liters equals 1000 milliliters because there are 1000 mL in 1 L.
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15 a (i): cm³
To convert liters to cubic centimeters (cm³):
1 liter
Therefore, liters . -
15 b (ii): m³
To convert liters to cubic meters (m³):
1 liter
Therefore, liters . -
15 c (iii): kL
To convert liters to kiloliters (kL):
1 kiloliter ,
So liters . -
15 d (iv): mL
To convert liters to milliliters (mL):
1 liter ,
So liters .
Question 16:
This question asks for the volume of a rectangular prism with length , width , and height , expressed in different units.
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16 a (i): cm³
The volume of a rectangular prism is given by in cubic centimeters.
The expression for the volume in is . -
16 b (ii): m³
To express the volume in cubic meters, convert the dimensions from centimeters to meters:
1 cm = 0.01 m,
So the volume ,
Simplifying, . -
16 c (iii): L
Since 1 liter ,
Volume in liters is . -
16 d (iv): kL
To convert to kiloliters, knowing 1 kL = 1000 L:
. -
16 e (v): mL
Since 1 mL = 1 cm³,
The volume in milliliters is .
Would you like any further details on the calculations? Here are 5 related questions to think about:
- How do you convert cubic meters to liters?
- If you know the volume in kL, how would you convert that to cm³?
- What is the difference between kiloliters and milliliters in terms of conversion?
- How would you calculate the volume of a cylinder instead of a rectangular prism?
- How does the conversion between units change if you're dealing with mass instead of volume?
Tip: Always remember to check unit consistency when performing volume calculations, especially when dimensions are provided in different units.
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Math Problem Analysis
Mathematical Concepts
Volume Conversion
Rectangular Prism Volume Calculation
Unit Conversion
Formulas
1 liter = 1000 cm³
1 liter = 0.001 m³
1 liter = 1000 mL
Volume of a rectangular prism = l × w × h
Theorems
Unit Conversion Theorem
Suitable Grade Level
Grades 6-8
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