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Grade 7 · unit review

Review: Circle and Prism Measures

Geometric measures answer different questions: circumference is boundary length, area covers a region, and volume counts space. A formula works only when its input dimensions and output units match the question being asked.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. A model circle has radius 7 cm. Use π≈3.14 to estimate circumference.
Need a hint?
  • A circle’s circumference is π times its diameter, equivalently 2π times its radius.
  • Do not substitute the radius into πd without first doubling it.
2. A model circle has radius 7 m. Use π≈3.14 to estimate its area.
Need a hint?
  • Circle area is πr².
  • The exponent applies to the radius, not to the whole product πr.
3. A rectangular prism measures 7 cm by 8 cm by 9 cm. What is its volume?
Need a hint?
  • A rectangular prism’s volume equals its base area times its perpendicular height.
  • Use three mutually perpendicular dimensions rather than adding edge lengths.
4. A closed rectangular box is 7 cm by 8 cm by 9 cm. What is its total surface area?
Need a hint?
  • A closed rectangular box has three pairs of congruent faces.
  • The word closed matters: an open-top box would omit one face.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. A model circle has radius 9 cm. Use π≈3.14 to estimate circumference. Candidate answers: (A) 18 cm (B) 254.34 cm (C) 28.26 cm (D) 56.52 cm. 2. A model circle has radius 9 m. Use π≈3.14 to estimate its area. Candidate answers: (A) 254.34 m² (B) 28.26 m² (C) 508.68 m² (D) 56.52 m². 3. A rectangular prism measures 9 cm by 10 cm by 11 cm. What is its volume? Candidate answers: (A) 30 cm³ (B) 598 cm³ (C) 90 cm³ (D) 990 cm³. 4. A closed rectangular box is 9 cm by 10 cm by 11 cm. What is its total surface area? Candidate answers: (A) 299 cm² (B) 598 cm² (C) 60 cm² (D) 990 cm².

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 56.52 cm. Circumference is 2πr. The diameter is 18 cm, so the estimate is 3.14×18=56.52 cm. This is length around, not area inside. 2. 254.34 m². Area is πr²: 3.14×9²=3.14×81=254.34 m². Square the radius before multiplying by π. 3. 990 cm³. One base has area 9×10=90 cm². Stack through a height of 11 cm: V=90×11=990 cm³. 4. 598 cm². Opposite faces occur in pairs. Add 2(9×10+9×11+10×11)=598 cm². All six faces count because the box is closed.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.