Math Problem Statement

If x is any number, then x liters is the same as 1000x milliliters because there are 1000 mL in 1 L. Write expressions for x liters in the following units (cm³, m³, kL, mL) and determine the volume of a rectangular prism in various units (cm³, m³, L, kL, mL).

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 xx liters in different units, knowing that xx liters equals 1000 xx milliliters because there are 1000 mL in 1 L.

  1. 15 a (i): cm³
    To convert liters to cubic centimeters (cm³):
    1 liter =1000cm3= 1000 \, \text{cm}^3
    Therefore, xx liters =1000xcm3= 1000x \, \text{cm}^3.

  2. 15 b (ii): m³
    To convert liters to cubic meters (m³):
    1 liter =0.001m3= 0.001 \, \text{m}^3
    Therefore, xx liters =0.001xm3= 0.001x \, \text{m}^3.

  3. 15 c (iii): kL
    To convert liters to kiloliters (kL):
    1 kiloliter =1000L= 1000 \, \text{L},
    So xx liters =x1000kL= \frac{x}{1000} \, \text{kL}.

  4. 15 d (iv): mL
    To convert liters to milliliters (mL):
    1 liter =1000mL= 1000 \, \text{mL},
    So xx liters =1000xmL= 1000x \, \text{mL}.


Question 16:

This question asks for the volume of a rectangular prism with length ll, width ww, and height hh, expressed in different units.

  1. 16 a (i): cm³
    The volume of a rectangular prism is given by V=l×w×hV = l \times w \times h in cubic centimeters.
    The expression for the volume in cm3\text{cm}^3 is V=l×w×hV = l \times w \times h.

  2. 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 V=(l×0.01)(w×0.01)(h×0.01)m3V = (l \times 0.01)(w \times 0.01)(h \times 0.01) \, \text{m}^3,
    Simplifying, V=l×w×h×106m3V = l \times w \times h \times 10^{-6} \, \text{m}^3.

  3. 16 c (iii): L
    Since 1 liter =1000cm3= 1000 \, \text{cm}^3,
    Volume in liters is V=l×w×h1000LV = \frac{l \times w \times h}{1000} \, \text{L}.

  4. 16 d (iv): kL
    To convert to kiloliters, knowing 1 kL = 1000 L:
    V=l×w×h1000×1000=l×w×h1,000,000kLV = \frac{l \times w \times h}{1000 \times 1000} = \frac{l \times w \times h}{1,000,000} \, \text{kL}.

  5. 16 e (v): mL
    Since 1 mL = 1 cm³,
    The volume in milliliters is V=l×w×hmLV = l \times w \times h \, \text{mL}.


Would you like any further details on the calculations? Here are 5 related questions to think about:

  1. How do you convert cubic meters to liters?
  2. If you know the volume in kL, how would you convert that to cm³?
  3. What is the difference between kiloliters and milliliters in terms of conversion?
  4. How would you calculate the volume of a cylinder instead of a rectangular prism?
  5. 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