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Test: Solids: volume and surface area

Dynamic tasks on volumes and surface areas of prisms, cylinders, pyramids and cones, including comprehension of their elements and scale effects.

Question qty: 10
Duration in minutes: 21
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Sample questions

  • A cylinder has radius r cm and height h cm. Calculate its volume using π ≈ 3.14.
  • If every length of similar solids is multiplied by k, by what factor does the volume increase?
  • A rectangular prism has base sides a cm and b cm and volume v cm³. Find its height.
  • A rectangular-based pyramid has base sides a cm and b cm and height h cm. Calculate its volume.
  • A closed cylinder has radius r cm and height h cm. Calculate its total surface area using π ≈ 3.14.
  • A cone has radius r cm and height h cm. Calculate its volume using π ≈ 3.14.
  • Which statement about solids is correct?
  • A rectangular prism measures a cm, b cm and h cm. Calculate its volume.

Volume and surface area of solids

Volume measures occupied space, while surface area is the sum of all outer faces. For a prism, V = base area × height; for a pyramid, divide this product by 3.

Selecting a formula

For a cylinder V = πr²h and for a cone V = πr²h/3. Identify the solid and its elements first. Scaling all lengths by k scales surface area by k² and volume by k³.

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