Circles Mastery Check Study Guide

Using the data table, what is the ratio of the circumference to the diameter of a circle?

• 1.50, for these specific circles only

• 1.50, which is true for all circles

• 3.14, for these specific circles only

• 3.14, which is true for all circles

Answer explanation

The ratio of circumference to diameter for any circle is a constant known as pi (π), approximately 3.14. Therefore, option D is correct as it applies to all circles.

Sirius wanted to add a fence around his hot tub. His hot tub has a radius of 3.5 feet. What is the approximate circumference of the fence?

• 11 feet

• 17 feet

• 22 feet

• 39 feet

Answer explanation

To find the circumference of a circle, use the formula C = 2πr. Here, r = 3.5 feet. Thus, C ≈ 2 × 3.14 × 3.5 ≈ 22 feet. Therefore, the approximate circumference of the fence is 22 feet.

Harry was looking at a pizza menu and ordered a circular pizza with a 12 inch diameter. What is the approximate area of the pizza?

• 19 square inches

• 38 square inches

• 113 square inches

• 452 square inches

Answer explanation

To find the area of a circular pizza, use the formula A = πr². The radius r is half the diameter, so r = 6 inches. Thus, A ≈ 3.14 × 6² = 113 square inches. Therefore, the correct answer is 113 square inches.

Ron wanted to put a sticker on top of his Frisbee that has a radius of 8 centimeters. What is the approximate area of the sticker?

• 25 square centimeters

• 201 square centimeters

• 50 square centimeters

• 804 square centimeters

Answer explanation

To find the area of the sticker, use the formula for the area of a circle: A = πr². With a radius of 8 cm, A ≈ 3.14 × (8)² = 201.06 square centimeters, which rounds to approximately 201 square centimeters.

A tire manufacturer needed to determine how long of a piece of rubber they needed to cut to make a bike tire. The bike wheel is about 50 centimeters in diameter. What is the approximate circumference of the wheel?

• 79 centimeters

• 157 centimeters

• 1963 centimeters

• 7850 centimeters

Answer explanation

To find the circumference of a circle, use the formula C = πd. For a diameter of 50 cm, C ≈ 3.14 × 50 = 157 cm. Thus, the approximate circumference of the bike wheel is 157 centimeters.

Hogwart's School for Witchcraft and Wizardry needed to paint a new circle in the center of their basketball court. The radius of the circle is 30 feet. What is the approximate circumference?

• 47 feet

• 94 feet

• 188 feet

• 707 feet

Answer explanation

To find the circumference of a circle, use the formula C = 2πr. Here, r = 30 feet. Thus, C ≈ 2 × 3.14 × 30 ≈ 188 feet. Therefore, the approximate circumference is 188 feet.

Hermione bought a circular cookie with a diameter of 6 inches. What is the approximate area of the cookie?

• 9.42 square inches

• 18.84 square inches

• 113.04 square inches

• 28.26 square inches

Answer explanation

To find the area of a circular cookie, use the formula A = πr². The radius r is half the diameter, so r = 3 inches. Thus, A ≈ 3.14 * (3)² = 28.26 square inches, which is the correct answer.

Circular pies at Perfect Pies come in 8-inch and 10-inch diameters. Which is closest to the difference in the areas of the pies? Use 3.14 for pi.

• 6.28 square inches

• 50.24 square inches

• 28.26 square inches

• 78.5 square inches

Answer explanation

To find the area difference, use A = πr². For the 8-inch pie, r = 4, area = 3.14 * 4² = 50.24 sq in. For the 10-inch pie, r = 5, area = 3.14 * 5² = 78.5 sq in. Difference = 78.5 - 50.24 = 28.26 sq in, closest to 28.26.

A circle has a circumference of 37.68 inches. What is the diameter of the circle? (Use 3.14 for π)

• 4 inches

• 8 inches

• 2 inches

• 12 inches

Answer explanation

To find the diameter, use the formula: Diameter = Circumference / π. Here, Diameter = 37.68 inches / 3.14 = 12 inches. Thus, the correct answer is 12 inches.

The circumference of a circle is 31.4 cm. What is the area of the same circle? (Hint: Calculate the diameter, then the radius, then the area)

• 10 square centimeters

• 314 square centimeters

• 78.5 square centimeters

• 31.4 square centimeters

Answer explanation

To find the area, first calculate the diameter using the circumference formula C = πd. Here, d = C/π = 31.4/π ≈ 10 cm. The radius r = d/2 = 5 cm. The area A = πr² ≈ 3.14 * 5² = 78.5 cm².