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Circle Area Exploration

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Circle Area Exploration

A community garden is redesigning its circular spaces. Use circle area and ratios to compare designs and make practical decisions. Use π ≈ 3.14 unless a question says otherwise; give units and round money to the nearest cent.

Plan the circular spaces

Use the area formula A = πr². Remember that radius is half the diameter.

1.A round pond has a radius of 2 m. What is its area using π ≈ 3.14? Include the square unit.

2.A circular planting bed has a diameter of 10 m. First find its radius, then calculate its area using π ≈ 3.14.

3.The pond radius and planting-bed radius are in the ratio 2:5. What is the ratio of their areas? Explain why the area ratio is not 2:5.

4.A second garden has the same shape as the first, but every length is 1.5 times as large. How many times as large is its circular bed's area?

1.5 times
2.25 times
3 times
4.5 times

Compare materials and costs

Use ratios to make fair comparisons between circular designs.

5.Two circular lawns have radii 3 m and 6 m. What is the ratio of the smaller lawn's area to the larger lawn's area in simplest form?

6.A circular garden has radius 4 m. Mulch costs $12 per square metre. Find the garden area and the total mulch cost, using π ≈ 3.14.

7.A designer doubles a circular bed's radius. True or false: the bed's area also doubles. Give the correct area multiplier.

TrueFalse

8.The ratio of two circular fountains' radii is 3:4. If the smaller fountain's area is 28.26 m² (using π ≈ 3.14), what is the larger fountain's area?

9.The garden team has 100 m² of turf. Can it cover a circular lawn with radius 5.5 m? Calculate the area and decide; use π ≈ 3.14.

10.A round seating area has diameter 8 m. A circular table in its centre has diameter 2 m. What area remains for seating, to 2 decimal places? Use π ≈ 3.14.

11.A circular bed has area 78.5 m² using π ≈ 3.14. Find its radius and diameter. Show how you work backwards from the area formula.