Math Problem Statement

When solving for the volume: V= lwh Where: l is length w is width h is height Unit of measurement is cubic centimeter or liter Practice exercises:

  1. How many grams of Aspirin are contained in 325 mg tab? The distance between Honolulu,Hawaii and Los Angeles, CA is 4,120km. How many frequent flyer miles will you earn by travelling between two cities? Carry out each of the ff Conversions
  2. 25L to dL
  3. 40 oz to g
  4. 32 inches to cm
  5. 1000km to mm
  6. 384 ft to inches
  7. 67 lbs to kg
  8. 2 tons to kg Solve for the volume
  9. l = 86 cm w= 50 cm h=105 cm
  10. l =6 inches w= 30cm h= 8inches

Solution

Let's tackle the exercises step by step:

1. How many grams of Aspirin are contained in a 325 mg tablet?

To convert milligrams (mg) to grams (g), recall that: 1 g = 1000 mg.

So, we convert 325 mg to grams: 325mg=3251000=0.325g.325 \, \text{mg} = \frac{325}{1000} = 0.325 \, \text{g}. Therefore, 0.325 grams of Aspirin are in the 325 mg tablet.


2. How many frequent flyer miles will you earn by traveling between Honolulu, Hawaii, and Los Angeles, CA (4,120 km)?

Typically, frequent flyer programs calculate miles directly based on kilometers traveled. Since 1 mile = 1.60934 kilometers, we convert kilometers to miles: Miles=4,1201.609342,561miles.\text{Miles} = \frac{4,120}{1.60934} \approx 2,561 \, \text{miles}. So, you would earn approximately 2,561 miles.


3. Convert 25 liters (L) to deciliters (dL).

Since 1 L = 10 dL, we multiply by 10: 25L×10=250dL.25 \, \text{L} \times 10 = 250 \, \text{dL}. Thus, 25 L = 250 dL.


4. Convert 40 ounces (oz) to grams (g).

Since 1 oz ≈ 28.3495 g, we multiply: 40oz×28.3495g/oz1,133.98g.40 \, \text{oz} \times 28.3495 \, \text{g/oz} \approx 1,133.98 \, \text{g}. So, 40 oz ≈ 1,134 g.


5. Convert 32 inches (in) to centimeters (cm).

Since 1 in = 2.54 cm, we multiply: 32in×2.54cm/in=81.28cm.32 \, \text{in} \times 2.54 \, \text{cm/in} = 81.28 \, \text{cm}. Thus, 32 inches = 81.28 cm.


6. Convert 1000 kilometers (km) to millimeters (mm).

We know: 1km=1,000,000mm.1 \, \text{km} = 1,000,000 \, \text{mm}. Thus: 1000km×1,000,000=1,000,000,000mm.1000 \, \text{km} \times 1,000,000 = 1,000,000,000 \, \text{mm}. So, 1000 km = 1 billion mm.


7. Convert 384 feet (ft) to inches.

Since 1 ft = 12 inches, we multiply: 384ft×12=4,608in.384 \, \text{ft} \times 12 = 4,608 \, \text{in}. Thus, 384 feet = 4,608 inches.


8. Convert 67 pounds (lbs) to kilograms (kg).

Since 1 lb ≈ 0.453592 kg, we multiply: 67lbs×0.453592kg/lb30.391kg.67 \, \text{lbs} \times 0.453592 \, \text{kg/lb} \approx 30.391 \, \text{kg}. So, 67 lbs ≈ 30.39 kg.


9. Convert 2 tons to kilograms.

Since 1 ton = 907.185 kg, we multiply: 2tons×907.185kg/ton=1,814.37kg.2 \, \text{tons} \times 907.185 \, \text{kg/ton} = 1,814.37 \, \text{kg}. Thus, 2 tons = 1,814.37 kg.


Solve for the Volume:

The formula for volume is V=l×w×hV = l \times w \times h.

10. l = 86 cm, w = 50 cm, h = 105 cm

V=86cm×50cm×105cm=451,500cm3.V = 86 \, \text{cm} \times 50 \, \text{cm} \times 105 \, \text{cm} = 451,500 \, \text{cm}^3. Thus, the volume is 451,500 cubic centimeters.

11. l = 6 inches, w = 30 cm, h = 8 inches

First, convert all dimensions to the same units (let's use cm). Since 1 inch = 2.54 cm: 6in×2.54=15.24cm,8in×2.54=20.32cm.6 \, \text{in} \times 2.54 = 15.24 \, \text{cm}, \quad 8 \, \text{in} \times 2.54 = 20.32 \, \text{cm}. Now calculate the volume: V=15.24cm×30cm×20.32cm9,286.82cm3.V = 15.24 \, \text{cm} \times 30 \, \text{cm} \times 20.32 \, \text{cm} \approx 9,286.82 \, \text{cm}^3. Thus, the volume is approximately 9,286.82 cubic centimeters.


Would you like more details or clarification on any step?

Here are some follow-up questions for further practice:

  1. Convert 500 mg to grams.
  2. Convert 10 miles to kilometers.
  3. If you travel 6,500 km, how many frequent flyer miles will you earn?
  4. Convert 5 tons to kilograms.
  5. Solve for the volume when l=15cm,w=25cm,h=12cml = 15 \, \text{cm}, w = 25 \, \text{cm}, h = 12 \, \text{cm}.

Tip: Always ensure all units are consistent before performing calculations!

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Volume Calculation
Basic Arithmetic
Metric and Imperial Systems

Formulas

V = l × w × h
Unit conversions (e.g., 1 inch = 2.54 cm, 1 g = 1000 mg, 1 lb ≈ 0.453592 kg)

Theorems

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Suitable Grade Level

Grades 6-8