3D Pythagoras' Theorem - Finding Volume WORKSHEET
Suitable for Year groups: Year 10, Year 11
GCSE Tier: Higher
Targeting grades: 6-7
Prerequisite knowledge: Pythagoras’ Theorem. Recognising right-angled triangles in 3D solids. Formulae for volume of prisms, pyramids, cones, and a cylinder.
3D Pythagoras' Theorem - Finding Volume WORKSHEET DESCRIPTION
This worksheet challenges students to apply Pythagoras’ Theorem in three dimensions to find the volumes of a variety of 3D shapes.
Learners will calculate missing lengths in order to complete volume calculations for prisms, pyramids, a cube, a cuboid, a cone, and a cylinder. The questions begin with tasks that require finding missing lengths on a single face before progressing to problems involving internal diagonals and perpendicular heights.
Each question requires identifying right triangles within the solids and using the theorem to determine the necessary dimensions before applying the appropriate volume formula.
Problems are designed to encourage spatial reasoning and multi-step thinking, with all answers rounded to three significant figures.
Learners will calculate missing lengths in order to complete volume calculations for prisms, pyramids, a cube, a cuboid, a cone, and a cylinder. The questions begin with tasks that require finding missing lengths on a single face before progressing to problems involving internal diagonals and perpendicular heights.
Each question requires identifying right triangles within the solids and using the theorem to determine the necessary dimensions before applying the appropriate volume formula.
Problems are designed to encourage spatial reasoning and multi-step thinking, with all answers rounded to three significant figures.
