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Practise the method.
Composite solids and inverse dimensions
Composite solids and inverse dimensions
Example 1
Two cuboids are joined without overlap. The lower cuboid is 8cm×4cm×9cm; the upper cuboid is 3cm×4cm×3cm. Find their total volume, in cm3.
Joined cuboids — front cross-sectionDiagram not to scaleShow worked answer
Answer: 324
Add the two non-overlapping volumes.
8×4×9+3×4×3=324cm3.
Example 2
A cuboid measures 9cm by 8cm by 5cm. A 3cm by 3cm rectangular corner is removed through the full depth 5cm. Find the remaining volume, in cm3.
L-shaped prismDiagram not to scaleShow worked answer
Answer: 315
Subtract the cut-out cross-section
multiply by depth: (9×8−3×3)×5=315cm3.
Example 3
A hollow cylinder has outer radius 8cm, inner radius 6cm and height 7cm. The hole runs through its full height. Find the material volume, in cm3. Use π=3. Give an exact answer.
Hollow cylinderDiagram not to scaleShow worked answer
Answer: 588
Subtract the inner cylinder: π(R2−r2)h.
Using π=3:3×(82−62)×7=588cm3.
Put it into practice.
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