Problems and solutions about Conversion of units – problems and solutions

1. Half a liter of fresh milk mixed with pudding sauce, then what is the volume of milk to be put in pudding sauce…

A. 5000 ml

B. 500 cc

C. 50 dm^{3}

D. 5 m^{3}

__Known :__

Volume of milk = 0.5 liter

__Wanted____ :__ 0.5 liter = ….. ml = ….. cm^{3} (cc) = ….. dm^{3} = ….. m^{3 }

__Solution :__

1 liter = 1000 milliliter (1000 ml)

1 liter = 0.001 m^{3 }= 1 dm^{3 }= 1000 cm^{3 }(1000 cc)

0.5 liter = (0.5)(1000 ml) = 500 ml

0.5 dm^{3} = (0.5)(1000 cc) = 500 cc

0.5 liter = 0.5 dm^{3 }= 0.0005 m^{3}

The correct answer is B.

2. If into 100 milliliters of liquid milk added 250 cc of water then how many mixtures are produced.

A. 12.5 dm^{3}

B. 1.25 dm^{3}

C. 3.5 dm^{3}

D. 0.35 dm^{3}

__Known :__

Volume of milk = 100 ml

Volume of water = 250 cc = 250 cm^{3}

__Wanted____ :__ 100 ml + 250 cc = ….. dm^{3}

__Solution :__

ml = milliliter

cc = cm^{3} = cubic centimeter

dm^{3} = cubic decimeter

1 dm^{3} = 1 liter = 1000 milliliters so that 100 milliliters = 100/1000 liters = 1/10 liters = 0.1 liter = 0.1 dm^{3}

1 dm^{3} = 1000 cm^{3} so that 250 cm^{3} = 250/1000 dm^{3} = 1/4 dm^{3} = 0.25 dm^{3}

100 ml + 250 cm^{3} = 0.1 dm^{3} + 0.25 dm^{3} = 0.35 dm^{3}

The correct answer is D.

3. A classroom whose length is 10 m and its width is 8 m, using ceramic as its floor. The size of the ceramic is 20 cm x 20 cm. The amount of ceramics on the floor in the room is ….

A. 20

B. 200

C. 2000

D. 20000

__Known :__

The size of a room :

Length = 10 meters

Width = 8 meters

Area of a room = 10 m x 8 m = 80 m^{2}

The size of a ceramic :

Length = 20 cm

Width = 20 cm

Area of a ceramic = 20 cm x 20 cm = 400 cm^{2}

Wanted : The number of ceramic used as the floor

__Solution :__

1 m = 100 cm

1 m^{2} = 10,000 cm^{2}

So 80 m^{2} = 80 x 10,000 cm^{2} = 800,000 cm^{2}

Number of ceramics = area of a room / area of a ceramic

Number of ceramics = 800,000 cm^{2} / 400 cm^{2}

Number of ceramics = 2000

The correct answer is C.

4. Every second as much as 4 cc of water dripped from a aquarium into a 5 liters container. The container is fully filled during ….. seconds.

A. 125 seconds

B. 200 seconds

C. 1250 seconds

D. 2000 seconds

__Known :__

1 liter = 1 dm^{3} = 1000 cm^{3}

Volume of water = 4 cc = 4 cm^{3}

Volume of container = 5 liters = 5 dm^{3} = 5 x 1000 cm^{3} = 5000 cm^{3}

__Wanted:__ Time interval the container full filled with water

__Solution :__

5000 cm^{3 }/ 4 cm^{3 }= 1250 seconds

The correct answer is C.

5. Mother bought drinking water 2 gallons (1 gallon = 19 liters) with price $2. If the volume of a cup of water is 200 ml, then determine the price of a cup of water.

__Known :__

1 gallon = 19 liters

2 gallon = 2 x 19 liters = 38 liters

1 liters = 1000 milliliters

38 liters = 38 x 1000 milliliters = 38,000 milliliters

1 glass of water = 200 milliliter

__Wanted :__ Price of a cup of water

__Solution :__

2 gallon of water = 38 liters = 38,000 milliliters

1 cup of water = 200 milliliters

38,000 ml / 200 ml = 190

In 2 gallon of water there are 190 cup of water.

Price of 2 gallon of water = $2

Price of 1 cup of water = $2 / 190 = $0.01

**1. Problem:** Convert 50 kilometers to miles. (1 mile ≈ 1.60934 km)

**Solution:** 50 km × (1 mile/1.60934 km) = 31.07 miles.

**2. Problem:** You have 2 liters of water. How many milliliters is that? (1 liter = 1,000 milliliters)

**Solution:** 2 liters × 1,000 ml/liter = 2,000 ml.

**3. Problem:** A baby weighs 8 pounds 5 ounces. Convert this to grams. (1 pound = 453.59237 grams and 1 ounce = 28.3495 grams)

**Solution:** 8 pounds × 453.59237 g/pound + 5 ounces × 28.3495 g/ounce = 3,628.73896 grams + 141.7475 grams = 3,770.48646 grams.

**4. Problem:** A tank holds 100 gallons of water. Convert this to liters. (1 gallon ≈ 3.78541 liters)

**Solution:** 100 gallons × 3.78541 liters/gallon = 378.541 liters.

**5. Problem:** Convert 250 centimeters to meters. (100 centimeters = 1 meter)

**Solution:** 250 cm ÷ 100 cm/meter = 2.5 meters.

**6. Problem:** A car travels at a speed of 55 miles per hour. Convert this speed to feet per second. (1 mile = 5,280 feet and 1 hour = 3,600 seconds)

**Solution:** 55 miles × 5,280 feet/mile ÷ 3,600 seconds = 81.78 feet/second.

**7. Problem:** A recipe requires 200 grams of sugar. Convert this to ounces. (1 ounce ≈ 28.3495 grams)

**Solution:** 200 grams × (1 ounce/28.3495 grams) = 7.055 ounces.

**8. Problem:** A room has an area of 300 square feet. Convert this to square meters. (1 square foot ≈ 0.092903 square meters)

**Solution:** 300 square feet × 0.092903 square meters/square foot = 27.8709 square meters.

**9. Problem:** You have a rope that is 150 inches long. Convert this to yards. (1 yard = 36 inches)

**Solution:** 150 inches ÷ 36 inches/yard = 4.1667 yards.

**10. Problem:** A bottle contains 500 milliliters of oil. Convert this to quarts. (1 quart ≈ 946.353 milliliters)

**Solution:** 500 milliliters × (1 quart/946.353 milliliters) = 0.5283 quarts.