Practice Maths

Topic Review — Surface Area and Volume

Mixed Practice — L31 – L33

This review covers all lessons in the Surface Area and Volume topic. Try each question before checking your answers.

Review Questions

  1. Surface area — fluency. Fluency

    1. Find the SA of a rectangular prism with l = 9 cm, w = 4 cm, h = 5 cm.
    2. Find the SA of a cylinder with r = 6 cm, h = 9 cm. Give the exact answer in terms of π.
    3. A cylinder has diameter 16 mm and height 25 mm. Find its SA to 1 d.p.
    4. A cube has SA = 216 cm². Find the side length.
    5. Find the SA of a triangular prism whose triangular face is a right triangle with legs 5 cm and 12 cm (hypotenuse 13 cm), and whose length is 20 cm.

  2. Volume — fluency. Fluency

    1. Find the volume of a cylinder with r = 3.5 cm and h = 10 cm. Give the answer to 2 d.p.
    2. Find the volume of a rectangular prism with l = 15 cm, w = 8 cm, h = 4 cm.
    3. A cylindrical tank has diameter 2.4 m and height 1.8 m. Find its volume in m³ to 3 d.p., then convert to litres.
    4. A triangular prism has a triangular cross-section with base 7 m and height 4 m. The prism is 9 m long. Find its volume.
    5. A cylinder has V = 500π cm³ and height 20 cm. Find its radius.

  3. Composite solids and hollow shapes. Understanding

    1. A solid is formed by stacking a cylinder (r = 2 cm, h = 5 cm) on top of a cube with side 4 cm. Find the total volume of the composite solid (to 2 d.p.).
    2. A hollow square prism has outer dimensions 10 cm × 10 cm × 30 cm and inner dimensions 8 cm × 8 cm × 30 cm. Find the volume of material in the walls.
    3. A cylindrical pipe (outer r = 6 cm, inner r = 5 cm, length 1.2 m) is to be painted on its outer curved surface only. Find the area to be painted in cm² (to 2 d.p.).
    4. A swimming pool is a rectangular prism 20 m × 10 m × 1.5 m deep. Find its capacity in litres, then find how long a pump delivering 1500 L/min takes to fill it.

  4. Real-world problem solving. Problem Solving

    1. A cylindrical water tank (r = 1.2 m, h = 2 m) needs to be painted on its outer curved surface and top lid. The paint covers 8 m² per litre and costs $22 per litre. Find the number of litres required (round up) and the total cost.
    2. A concrete cylindrical pillar has radius 25 cm and height 3.5 m. How many cubic metres of concrete are needed (to 3 d.p.)? If concrete costs $280 per m³, what is the cost?
    3. A storage box (rectangular prism: 60 cm × 45 cm × 40 cm) is to be wrapped in paper, with 20% extra for overlaps. Paper costs $3.20 per square metre. Find the total cost of paper (to the nearest cent).
    4. A manufacturer makes cylindrical aluminium cans with r = 3.5 cm and h = 12 cm. Each can requires aluminium costing $0.005 per cm². Find the SA of one can and the material cost. If 5000 cans are made, what is the total cost?

  5. Mixed extended response. Problem Solving

    1. A farmer's water trough is in the shape of a triangular prism lying on its side. The cross-section is an isosceles triangle with base 0.8 m and perpendicular height 0.5 m. The trough is 4 m long.
      1. Find the volume of the trough in m³ and in litres.
      2. The trough is currently half full. How many litres does it contain?
      3. The inside of the trough (all three rectangular faces and two triangular ends) is to be waterproofed. Find the total inner surface area.
    2. Two cylindrical silos are used to store grain. Silo A has r = 4 m, h = 10 m. Silo B has r = 5 m, h = 6.4 m.
      1. Which silo holds more grain? Show calculations.
      2. The curved surface of each silo needs weather-proofing sealant at $15 per m². Which silo costs less to seal, and by how much?
      3. If Silo A is 60% full and Silo B is 75% full, how many litres of grain are stored in total?
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