Geometry
Circle measurements worksheets
Find radius, diameter, circumference and area in nine circles from a supplied radius or diameter. Choose any of five units, use pi = 3.14, and optionally print the formulas.
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Prism and cylinder volume worksheets
Find the volume of nine cubes, rectangular, triangular, trapezoidal, regular pentagonal or regular hexagonal prisms and cylinders, with selectable problem types and units.
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Find each volume using calculator pi for cylinders. Keep intermediate values unrounded and round only the final answer to the nearest hundredth. Diagrams are not to scale.
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Customize this worksheetFind base area, then multiply by the distance between bases
Every sheet has nine solids. Mixed practice includes all seven prism kinds plus one radius-given and one diameter-given cylinder. The legend uses L for the distance between prism bases and h for an altitude inside a triangular or trapezoidal base.
Compute each base area before multiplying by L or cylinder height H. For regular bases, use A = sqrt(25 + 10sqrt(5)) × s² / 4 for a pentagon and A = 3sqrt(3) × s² / 2 for a hexagon. Use full calculator pi for cylinders and round only the final volume to the nearest hundredth.
Learning objective
What this activity builds
Identify a solid’s base area and multiply by the distance between parallel bases, using full calculator pi and rounding only the final volume to the nearest hundredth.
Worked example
A cylinder has diameter 6 cm and height 8 cm. What is its volume?
226.19 cm³.
The radius is 3 cm. Use V = pi × 3² × 8 with the calculator value of pi, then round the final result 226.194... to 226.19 cm³.
Teaching notes
Make the practice count
- Treat L as the distance between the two parallel prism bases; it is different from h, the altitude drawn inside a triangular or trapezoidal base.
- For a regular pentagon use base area = sqrt(25 + 10sqrt(5)) × s² / 4; for a regular hexagon use base area = 3sqrt(3) × s² / 2.
- Use the supplied regular-polygon side length to compute base area; the drawing does not supply a numerical apothem.
- For cylinders, halve a supplied diameter before squaring and keep the calculator value of pi until the final rounding step.
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