TEKS 7.9B Worksheets — Grade 7 Determine the circumference and area of circles

Lily is organizing a science fair at her school in Houston. She plans to use a round table for her display that has a diameter of 6 feet. What is the area of the top of the table, in square feet? Use 3.14 for pi.

1. 28.26 ✓
2. 18.84
3. 12.56
4. 37.68

Why: To find the area of a circle, we use the formula A = pi * r^2. First, we need to find the radius, which is half of the diameter. The diameter is 6 feet, so the radius (r) is 6 / 2 = 3 feet. Now we can plug in the values into the formula: A = 3.14 * (3)^2 = 3.14 * 9 = 28.26 square feet. Therefore, the correct answer is 28.26.

Santiago is planning a picnic at Palo Duro Canyon and wants to set up a circular area for seating. He decides to use a circle with a diameter of 10 feet. What is the area of the circular seating area he plans to create? Use 3.14 for π.

1. 78.5 ✓
2. 31.4
3. 25.0
4. 15.7

Why: To find the area of a circle, use the formula A = πr². First, find the radius by dividing the diameter by 2. The radius is 10 / 2 = 5 feet. Now plug the radius into the formula: A = 3.14 * (5)² = 3.14 * 25 = 78.5 square feet. Thus, the correct answer is 78.5.

Sofia is planning to plant a circular flower garden in her backyard in Austin, Texas. If the radius of the garden is 4.5 feet, which expression best represents the area of the garden in square feet?

1. 20.25π ✓
2. 28.26
3. 18π
4. 56.52

Why: To find the area of a circle, use the formula A = πr². For Sofia's garden, the radius is 4.5 feet. First, calculate the square of the radius: 4.5 * 4.5 = 20.25. Then multiply by π: A = π * 20.25, which is best represented as 20.25π. Therefore, the correct answer is 20.25π.

Carlos is planting a circular garden in his backyard in McAllen, Texas. The garden has a radius of 3 feet. If Carlos wants to put a fence around the garden, which of the following best represents the total length of the fence he needs to purchase?

1. 18.84 feet ✓
2. 9.42 feet
3. 9 feet
4. 28.26 feet

Why: To find the length of the fence, we need to calculate the circumference of the circular garden. The formula for circumference is C = 2 * π * r, where r is the radius. Given that the radius is 3 feet, we have C = 2 * π * 3 = 6π feet. Using 3.14 for π, the total length is approximately 6 * 3.14 = 18.84 feet. Therefore, the correct answer is 18.84 feet.

Camila is planning a fundraiser at her school in Texas to support local wildlife conservation efforts. She wants to create a circular garden to attract native birds. If the radius of the garden is 3.5 feet, what is the area of the garden? Use 3.14 for π.

1. 38.465 ✓
2. 12.25
3. 21.56
4. 15.4

Why: To find the area of the circular garden, use the formula A = πr². Substituting the values, A = 3.14 * (3.5)². First, calculate (3.5)² which equals 12.25. Then, multiply 3.14 by 12.25 to get approximately 38.465. Thus, the area of the garden is 38.465 square feet.

Hugo is creating a circular flower bed in his backyard in Austin. The radius of the flower bed is 4 feet. He also wants to add a border around the flower bed that is 1 foot wide. What is the total area of the flower bed including the border? (Use 3.14 for π)

1. 78.5 ✓
2. 65.1
3. 50.3
4. 32.0

Why: To find the total area of the flower bed including the border, first calculate the radius including the border. The total radius is 4 feet + 1 foot = 5 feet. Now, use the formula for the area of a circle, A = π * r^2. Substituting the radius: A = 3.14 * (5^2) = 3.14 * 25 = 78.5 square feet. Therefore, the correct answer is 78.5.

Ximena is planting a circular flower garden in her backyard in Austin, Texas. The radius of the garden is 4.5 feet. If she wants to put a fence around the garden, how much fencing will she need? Use 3.14 for π.

1. 28.26 ✓
2. 18.84
3. 14.13
4. 50.88

Why: To find the circumference of Ximena's circular garden, use the formula C = 2πr. Here, the radius (r) is 4.5 feet. Plugging in the values gives C = 2 * 3.14 * 4.5 = 28.26 feet. Therefore, she will need 28.26 feet of fencing.

Sofia is helping her father plant a garden in their backyard in Texas. The garden is in the shape of a circle with a radius of 3 feet. If they want to put a border around the garden, how many feet of border will they need to go around the garden? Use 3.14 for π.

1. 18.84 ✓
2. 9.42
3. 28.26
4. 12.56

Why: To find the circumference of a circle, use the formula C = 2πr. With a radius (r) of 3 feet, the calculation is C = 2 * 3.14 * 3 = 18.84 feet. Therefore, the border needed is 18.84 feet.