Volume with Fractional Edge Lengths · MCAP 6.G.A.2

Learning Goal: Find the volume of right rectangular prisms, including ones with fraction or mixed-number edge lengths, using V = l·w·h and V = B·h.

Vocabulary

volumeThe amount of space inside a 3D solid, measured in cubic units (like cubic inches, in³).

rectangular prismA box-shaped solid with 6 flat rectangular faces (length, width, and height).

unit cubeA cube with each edge 1 unit long; its volume is 1 cubic unit.

base area (B)The area of the bottom face of a prism, found by length × width.

What You Need to Know

Volume of a rectangular prism = length × width × height (V = l·w·h).
You can also use V = B·h, where B is the area of the base (length × width) and h is the height.
Both formulas give the same answer because B = l·w, so B·h = l·w·h.
To multiply mixed numbers, change them to improper fractions first (example: 4 1/2 = 9/2).
Multiply across: top × top over bottom × bottom, then simplify or change back to a mixed number.
Volume is always written in cubic units, such as cm³, in³, or m³.

Worked Example I Do — watch how it works

A box has a length of 4 1/2 in, a width of 3 in, and a height of 2 1/2 in. Find its volume.

Step 1. Change mixed numbers to improper fractions: 4 1/2 = 9/2 and 2 1/2 = 5/2.
Step 2. Use V = l·w·h: V = 9/2 × 3 × 5/2.
Step 3. Multiply: (9 × 3 × 5) / (2 × 2) = 135/4 = 33 3/4 in³.

Answer: 33 3/4 in³ (33.75 in³)

Guided Practice We Do — try it together

1. A prism has length 5 cm, width 2 cm, and height 1/2 cm. Find the volume.
💡 Hint: Multiply 5 × 2 first, then multiply by 1/2.
2. A box has a base area B = 12 ft² and a height of 3 1/2 ft. Find the volume using V = B·h.
💡 Hint: Change 3 1/2 to 7/2, then multiply 12 × 7/2.
3. A prism has length 3 1/2 in, width 2 in, and height 1 1/2 in. Find the volume.
💡 Hint: Change to improper fractions: 7/2, 2/1, 3/2, then multiply all three.

Independent Practice You Do — show your work

1. A box has length 6 m, width 4 m, and height 3 m. Find the volume.
2. A prism has length 2 1/2 cm, width 4 cm, and height 3 cm. Find the volume.
3. A box has a base area of 15 in² and a height of 2 1/3 in. Use V = B·h.
4. A prism has length 3/4 ft, width 2 ft, and height 4 ft. Find the volume.
5. A box has length 4 1/2 cm, width 2 1/2 cm, and height 2 cm. Find the volume.

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.G.A.2.

Item 1Selected Response6.G.A.2

A rectangular prism has length 3 in, width 2 in, and height 1 1/2 in. What is its volume?

Select the correct answer.

○ A. 6 in³○ B. 6 1/2 in³○ C. 9 in³○ D. 12 in³

Item 2Selected Response6.G.A.2

A storage bin has a base area of 8 ft² and a height of 4 1/2 ft. What is its volume?

Select the correct answer.

○ A. 12 1/2 ft³○ B. 18 ft³○ C. 32 ft³○ D. 36 ft³

Item 3Constructed Response6.G.A.2

A jewelry box is 2 1/2 in long, 2 in wide, and 1 1/2 in tall. What is its volume?

Enter your answer in the space provided. Show your work.

Enter your answer:

Teacher Answer Key (click to show)

Independent 1	72 m³
Independent 2	30 cm³
Independent 3	35 in³
Independent 4	6 ft³
Independent 5	22 1/2 cm³
Item 1 · 6.G.A.2	C — V = 3 × 2 × 3/2 = 6 × 3/2 = 18/2 = 9 in³.
Item 2 · 6.G.A.2	D — V = B·h = 8 × 9/2 = 72/2 = 36 ft³.
Item 3 · 6.G.A.2	7 1/2 in³ — V = 5/2 × 2 × 3/2 = 30/4 = 7 1/2 in³.

Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.G.A.2