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.
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Sample questions
- A closed cylinder has radius ___ cm and height ___ cm. Calculate its total surface area using π ≈ 3.14.
- If every length of similar solids is multiplied by ___, by what factor does the volume increase?
- A rectangular prism measures ___ cm, ___ cm and ___ cm. Calculate its volume.
- A rectangular prism has base sides ___ cm and ___ cm and volume ___ cm³. Find its height.
- A cylinder has radius ___ cm and height ___ cm. Calculate its volume using π ≈ 3.14.
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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