Here are the step-by-step solutions for each problem on the worksheet.
1. Gianna's Walk (Circumference)
*
Goal: Find the distance around the pond (circumference).
*
Given: Diameter ($d$) = 29 meters.
*
Formula: Circumference = $\pi \times d$
*
Calculation:
* $C = 3.14159 \times 29$
* $C \approx 91.106$
*
Rounding: Round to the nearest tenth. The digit in the tenths place is 1, and the next digit is 0, so it stays 1.
*
Result: 91.1 meters.
2. Julieta's Walk (Circumference)
*
Goal: Find the distance around the pond (circumference).
*
Given: Diameter ($d$) = 36 meters.
*
Formula: Circumference = $\pi \times d$
*
Calculation:
* $C = 3.14159 \times 36$
* $C \approx 113.097$
*
Rounding: Round to the nearest tenth. The digit in the tenths place is 0, and the next digit is 9, so we round up to 1.
*
Result: 113.1 meters.
3. Jesse's Fence (Cost based on Circumference)
*
Goal: Find the total cost of the fence.
*
Given: Radius ($r$) = 17 feet. Cost = \$8 per foot.
*
Step 1: Find the length of the fence (Circumference).
* Formula: $C = 2 \times \pi \times r$
* $C = 2 \times 3.14159 \times 17$
* $C = 6.28318 \times 17$
* $C \approx 106.814$ feet.
*
Step 2: Calculate the cost.
* Cost = Length $\times$ Price per foot
* Cost = $106.814 \times 8$
* Cost $\approx 854.51$
*
Rounding: Round to the nearest dollar. Since .51 is 50 cents or more, we round up.
*
Result: \$855.
4. Sydney's Fence (Cost based on Circumference)
*
Goal: Find the total cost of the fence.
*
Given: Radius ($r$) = 37 meters. Cost = \$12 per meter.
*
Step 1: Find the length of the fence (Circumference).
* Formula: $C = 2 \times \pi \times r$
* $C = 2 \times 3.14159 \times 37$
* $C = 6.28318 \times 37$
* $C \approx 232.478$ meters.
*
Step 2: Calculate the cost.
* Cost = Length $\times$ Price per meter
* Cost = $232.478 \times 12$
* Cost $\approx 2789.73$
*
Rounding: Round to the nearest dollar. Since .73 is 50 cents or more, we round up.
*
Result: \$2,790.
5. Brooklyn's Target (Area)
*
Goal: Find the area of the circular target.
*
Given: Diameter ($d$) = 14 feet.
*
Step 1: Find the radius.
* Radius is half of the diameter.
* $r = 14 / 2 = 7$ feet.
*
Step 2: Calculate Area.
* Formula: Area = $\pi \times r^2$
* Area = $3.14159 \times 7^2$
* Area = $3.14159 \times 49$
* Area $\approx 153.938$
*
Rounding: Round to the nearest tenth. The digit in the tenths place is 9, and the next digit is 3, so it stays 9.
*
Result: 153.9 square feet.
6. Sophie's Window (Area)
*
Goal: Find the area of the glass needed.
*
Given: Diameter ($d$) = 16 feet.
*
Step 1: Find the radius.
* Radius is half of the diameter.
* $r = 16 / 2 = 8$ feet.
*
Step 2: Calculate Area.
* Formula: Area = $\pi \times r^2$
* Area = $3.14159 \times 8^2$
* Area = $3.14159 \times 64$
* Area $\approx 201.062$
*
Rounding: Round to the nearest tenth. The digit in the tenths place is 0, and the next digit is 6, so we round up to 1.
*
Result: 201.1 square feet.
Final Answer:
1. 91.1 meters
2. 113.1 meters
3. $855
4. $2,790
5. 153.9 square feet
6. 201.1 square feet
Parent Tip: Review the logic above to help your child master the concept of circumference word problems worksheet.
