Field Notesgrade 7 math
Back to Circles

Solution key: Around and inside

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1 of 8 · circles-c01

A circle has radius 9. What is the diameter?

  1. The radius is the distance from the center to the edge.
  2. The diameter is the full cut through the center, so it is twice the radius.
  3. 2 times 9 is 18.
  1. The diameter is 18.
  2. Check: Half of diameter 18 is the given radius 9.

Answer: 18

2 of 8 · circles-c02

A circle has diameter 10. Using π = 3.14, what is the circumference?

  1. Circumference is the distance around the circle.
  2. When you know the diameter, multiply it by π. This problem asks us to use 3.14 as an approximation of π.
  3. 3.14 times 10 is 31.4.
  1. The circumference is 31.4.
  2. Check: 31.4 ÷ 10 = 3.14, the approximation of π used in this problem.

Answer: 31.4 units

3 of 8 · circles-c03

A circle has radius 4. Using π = 3.14, what is the circumference?

  1. You were given the radius, not the diameter.
  2. The distance around is 2 times π times the radius, because two radii make a diameter.
  3. 2 times 3.14 is 6.28, and 6.28 times 4 is 25.12.
  1. The circumference is 25.12.
  2. Check: Diameter 2×4=8 gives 3.14×8=25.12.

Answer: 25.12 units

4 of 8 · circles-c04

A circle has radius 5. Using π = 3.14, what is the area?

  1. Area is the space inside the circle, and it uses the radius squared.
  2. Square the radius first: 5 times 5 is 25.
  3. Then multiply by π: 3.14 times 25 is 78.5.
  1. The area is 78.5.
  2. Check: 78.5÷3.14=25=5×5. Area measures a surface, so use square units.

Answer: 78.5 sq units

5 of 8 · circles-c05

A circle has diameter 8. Using π = 3.14, what is the area?

  1. Area needs the radius, but the problem gives the diameter.
  2. Radius is half the diameter, so half of 8 is 4.
  3. Square that radius: 4 times 4 is 16. Then 3.14 times 16 is 50.24.
  1. The area is 50.24.
  2. Check: Twice the radius 4 is diameter 8; square 4, not 8.

Answer: 50.24 sq units

6 of 8 · circles-c06

A circle has circumference 31.4. Using π = 3.14, what is the diameter?

  1. Circumference is π times the diameter, so the diameter is the circumference divided by π.
  2. Divide 31.4 by 3.14.
  3. 3.14 times 10 is 31.4, so the division is 10.
  1. The diameter is 10.
  2. Check: 3.14×diameter 10=31.4, the given circumference.

Answer: 10

7 of 8 · circles-c07

A semicircle has diameter 10. Using π = 3.14, what is the area?

  1. A semicircle is half a circle. We know the diameter is 10 and we use 3.14 for π. Find the area inside.
  2. The radius is half the diameter: 10 ÷ 2 = 5.
  3. A full circle's area is π times the radius multiplied by itself. 5 × 5 = 25, and 3.14 × 25 = 78.5.
  1. The semicircle is half of that area: 78.5 ÷ 2 = 39.25 square units.
  2. Check: 39.25 × 2 = 78.5, and 78.5 ÷ 3.14 = 25, which is 5 × 5.

Answer: 39.25 sq units

8 of 8 · circles-c08

A circle has radius 6. What is the area? Leave π in the answer instead of using 3.14. For example, eight times π is typed 8pi.

  1. Leave π in the answer this time. Do not swap in 3.14.
  2. Area is π times radius squared.
  3. 6 times 6 is 36, so the area is 36 times π.
  1. Write that as 36pi.
  2. Check: π×6×6=36π; keep π exact and type 36pi.

Answer: 36pi