M2 · Solve volume and capacity problems with SI and imperial units

Alberta Grade 11 Mathematics

Measurement

Choose a volume model, keep units consistent, and interpret the result

What you will learn

• Calculate the volume of a rectangular prism using consistent units.
• Distinguish volume from capacity and connect their units.
• Solve volume and capacity problems using provided SI and imperial conversions.
• Check that an answer has suitable units and is reasonable.

1. Start with the shape and its units

• A rectangular prism uses three dimensions: length, width, and height.
• Use matching units in a volume calculation.
• Volume is measured in cubic units; capacity is often measured in litres or gallons.

2. Convert only when the units require it

• Convert all dimensions to one unit before multiplying.
• A conversion for length is not automatically the conversion for volume.
• An approximate factor leads to an approximate answer.

3. Interpret the answer and check it

• State whether the result is volume or capacity.
• Include units and sensible rounding.
• Compare the result with the size of the object and the information given.

Worked example

A water tank for a garden

1. Identify the model
   The tank is a rectangular prism. All three measurements are already in metres, so they can be multiplied directly.
   $$V=lwh$$
2. Calculate the volume
   Multiply the three dimensions. The unit is cubic metres because metres are multiplied three times.
   $$V=(1.2)(0.8)(0.5)=0.48\text{ m}^3$$
3. Convert to capacity
   Each cubic metre holds 1,000 litres. Multiply by 1,000 to express this tank's capacity in litres.
   $$0.48\text{ m}^3=480\text{ L}$$

Worked example

A shipping container measured in inches

1. Convert each dimension
   The requested unit is cubic feet. Convert each inside dimension from inches to feet before multiplying. The converted dimensions are 2 ft, 1.5 ft, and 1 ft. 24 in=2 ft,\quad18 in=1.5 ft,\quad12 in=1 ft
2. Find the volume
   Use the rectangular-prism volume rule with all three dimensions in feet.
   $$V=(2)(1.5)(1)=3\text{ ft}^3$$
3. Check the result
   The box is 2 ft long, 1.5 ft wide, and 1 ft high. A volume of 3 cubic feet fits those dimensions.
   $$V=3\text{ ft}^3$$

Worked example

Converting an imperial tank capacity

1. Calculate cubic volume
   The dimensions use feet, so their product is in cubic feet.
   $$V=(3)(2)(1)=6\text{ ft}^3$$
2. Convert to imperial gallons
   Multiply the volume in cubic feet by the supplied approximate conversion factor.
   $$6\text{ ft}^3\times6.23\frac{\text{imp gal}}{\text{ft}^3}\approx37.38\text{ imp gal}$$
3. Convert to litres
   Use the given litres-per-imperial-gallon factor. Round to the nearest litre because the starting conversion is approximate.
   $$37.38\text{ imp gal}\times4.546\frac{\text{L}}{\text{imp gal}}\approx170\text{ L}$$

Common mistakes and how to avoid them

Lesson summary

• For a rectangular prism, multiply length, width, and height.
• Use matching units in the multiplication and report a cubic unit.
• Convert volume to capacity with a stated conversion factor when required.
• Include units and check whether the size of the answer makes sense.

Check your understanding

Key terms

Volume

The amount of three-dimensional space occupied by a solid or inside a container.

Capacity

The amount a container can hold, often reported as a liquid measure.

Rectangular prism

A solid with six rectangular faces, such as a box.

Conversion factor

A stated relationship used to express a measurement in a different unit.

Continue through Math 20-3

View the complete Math 20-3 Alberta Grade 11 Mathematics curriculum and lessons

• G1 · Solve problems involving two or three right triangles
• G2 · Solve practical scale and scale-diagram problems
• G3 · Model 3-D objects and draw their top, front, and side views
• G4 · Draw and describe simple exploded views and scaled components
• N1 · Use and verify strategies for numerical puzzles and games
• N3 · Explain and calculate compound-interest growth

Tutor support for M2 · Solve volume and capacity problems with SI and imperial units

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برای مبحث M2 · مسئله‌های حجم و گنجایش را با واحدهای متریک و امپریال حل کنید در درس Math 20-3، سؤال و تلاش خود را همراه بیاورید. در جلسه می‌توانید گام‌های تلاش خود را نشان دهید و آن را با یک نمونهٔ حل‌شده مقایسه کنید. راهنمای معلم ریاضی را ببینید یا جلسهٔ معارفهٔ رایگان ۳۰ دقیقه‌ای درخواست کنید. زمان جلسه پس از پذیرش معلم قطعی می‌شود.

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation M2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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