Test
Pythagoras in solids
Dynamic tasks on space diagonals, cone slant height, pyramid apothem, sphere area and volume.
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Sample questions
- A rectangular prism measures ___ cm, ___ cm and ___ cm. Find its space diagonal.
- A rectangular prism has base sides ___ cm and ___ cm and space diagonal ___ cm. Find its height.
- A cone has radius ___ cm and height ___ cm. Find its slant height.
- A regular square pyramid has base side ___ cm and height ___ cm. Find the slant height of a face.
- A cylinder’s axial section is a rectangle of diameter based on radius ___ cm and height ___ cm. Find its diagonal.
Pythagoras in solids
A spatial distance can often be found by applying the Pythagorean theorem twice. The space diagonal of a rectangular prism is d = √(a² + b² + h²). A cone slant height, radius and vertical height form a right triangle.
Solids and formulas
The apothem of a regular pyramid is found from half a base side and the vertical height. A sphere has surface area S = 4πr² and volume V = 4πr³/3. First identify the right triangle and distinguish vertical height, lateral edge and apothem.
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