Topic Review — Volume

Review Questions

1. Prisms and solids: Fluency

   1. What is the name of a prism with a triangular cross-section?
   2. A solid has two circular bases. Is it a prism?
   3. How many faces does a rectangular prism have?
   4. True or False: a cube is a special type of rectangular prism.

2. Calculate the volume using V = l × w × h: Fluency

   1. 6 cm × 4 cm × 3 cm
   2. 10 m × 5 m × 2 m
   3. A cube with side length 8 cm
   4. 7 cm × 3 cm × 4 cm
   5. 12.5 cm × 4 cm × 2 cm

3. Volume using base area: Understanding

   1. A prism has a base area of 24 cm² and a height of 5 cm. Find the volume.
   2. A rectangular prism is filled with 6 layers of unit cubes, with 15 cubes in each layer. What is the volume?
   3. A prism has a volume of 180 cm³ and a base area of 30 cm². Find the height.

4. Find the missing dimension: Understanding

   1. V = 120 cm³, l = 10 cm, w = 4 cm. Find h.
   2. V = 180 cm³, l = 12 cm, h = 3 cm. Find w.
   3. A cube has a volume of 125 cm³. Find the side length.

5. A fish tank measures 60 cm × 30 cm × 40 cm. Problem Solving

   1. What is the total volume of the tank in cm³?
   2. How many litres does it hold when full? (1000 cm³ = 1 L)
   3. The tank is filled to 75% capacity. How many litres is that?
   4. 18 litres evaporate. How many litres remain?

6. Convert between units of volume: Fluency

   1. 3 L = ___ mL
   2. 4500 mL = ___ L
   3. 2.75 L = ___ mL
   4. 250 cm³ = ___ mL (1 cm³ = 1 mL)

7. Compare two boxes: Box A is 10 cm × 6 cm × 4 cm. Box B is 8 cm × 8 cm × 3 cm. Understanding

   1. Find the volume of each box.
   2. Which box has the greater volume?
   3. By how many cm³ is it larger?

8. A swimming pool is 25 m long, 10 m wide, and 1.8 m deep. Problem Solving

   1. Calculate the volume of the pool in m³.
   2. How many kilolitres of water does it hold? (1 m³ = 1 kL)
   3. Water costs $1.50 per kL. How much does it cost to fill the pool?
   4. It takes 3 hours to fill. How many kL per hour does the hose deliver?

9. Explain and reason: Understanding

   1. Two prisms have the same volume of 240 cm³. Prism A has a base area of 40 cm². Prism B has a height of 6 cm. Find the height of A and the base area of B.
   2. True or False: if you double the length of a rectangular prism, the volume doubles. Explain.
   3. A cube has a volume of 343 cm³. What is its side length?

10. Stacking boxes: small boxes each measure 5 cm × 4 cm × 3 cm. A large crate measures 30 cm × 20 cm × 12 cm. Problem Solving

    1. What is the volume of one small box?
    2. What is the volume of the large crate?
    3. How many small boxes fit perfectly in the crate?