Circles and Pi

What is the formula to calculate the circumference of a circle?

• 2 * radius

• pi * radius

• radius * radius

• 2 * pi * radius

Answer explanation

The question asks for the formula to calculate the circumference of a circle. The correct formula is '2 * pi * radius'. In this formula, '2' is the multiplier, 'pi' is a constant approximately equal to 3.14, and 'radius' is the distance from the center of the circle to its edge. Therefore, to find the circumference, you multiply twice the value of pi by the radius.

Tags

CCSS.7.G.B.4

What is the formula to calculate the area of a circle?

• A = πd

• A = r^2

• A = 2πr

• A = πr^2

Answer explanation

The question asks for the formula to calculate the area of a circle. The correct answer is 'A = πr^2'. This formula represents the area (A) of a circle as a function of its radius (r). The symbol π represents Pi, approximately 3.14159. The other options are not correct, they represent different mathematical relationships involving circles, not their area.

Tags

CCSS.7.G.B.4

What is the radius of a circle if its diameter is 10 units?

• 5

• 7

• 2.5

• 12

Answer explanation

The question asks for the radius of a circle given that its diameter is 10 units. In circle geometry, the radius is exactly half of the diameter. Therefore, if the diameter is 10 units, then the radius would be 5 units. Hence, the correct answer is 5.

Tags

CCSS.7.G.B.4

What is the diameter of a circle if its radius is 5 units?

• 15

• 12

• 10

• 8

Answer explanation

The diameter of a circle is simply twice the radius. So, if the radius of the circle is given as 5 units, the diameter would be 2 times 5, which equals 10 units. Therefore, the correct answer to the question is 10.

Tags

CCSS.7.G.B.4

What is the value of Pi (π)?

• 3.14159

• 3.1416

• 22/7

• 3.14

Answer explanation

The value of Pi (π) is approximately equal to 3.14159, which is a mathematical constant used to represent the ratio of a circle's circumference to its diameter. While other options are close approximations, 3.14159 is the most accurate value listed.

Tags

CCSS.HSG.GMD.A.1

What is the significance of Pi in circle calculations?

• Pi is used to calculate the volume of circles.

• Pi is used to calculate the angles of circles.

• Pi is used to calculate the diameter of circles.

• Pi is used to calculate the circumference, area, and other properties of circles.

Answer explanation

Pi (approximately 3.14159) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It plays a crucial role in calculating various properties of circles, such as circumference (C = 2 * Pi * r) and area (A = Pi * r^2), where 'r' is the radius of the circle. The other options mentioned are not the primary uses of Pi in circle calculations.

Tags

CCSS.HSG.GMD.A.1

Calculate the circumference of a circle with a radius of 8 units. (Use π = 3.14)

• 25.12

• 64.32

• 50.24

• 40.48

Answer explanation

The question asks to calculate the circumference of a circle with a radius of 8 units using π = 3.14. The formula for the circumference is C = 2πr. Substituting the given values, we get C = 2 * 3.14 * 8, which equals 50.24. So, the correct option is 50.24.

Tags

CCSS.7.G.B.4

Calculate the area of a circle with a diameter of 12 units. (Use π = 3.14)

• 37.68

• 144

• 113.04

• 6.28

Answer explanation

To calculate the area of a circle, we use the formula A = πr², where A is the area and r is the radius. The given diameter is 12 units, so the radius is 6 units. Using π = 3.14, the area is calculated as A = 3.14 * (6²) = 3.14 * 36 = 113.04 square units, which is the correct answer.

Tags

CCSS.7.G.B.4

Calculate the radius of a circle with an area of 154 square units. (Use π = 3.14)

• 12.00

• 5.00

• 9.00

• 7.00

Answer explanation

To find the radius of a circle with an area of 154 square units, we use the formula A = πr², where A is the area and r is the radius. Given A = 154 and π = 3.14, we can solve for r. By plugging the values and isolating r, we get r² = 154 / 3.14, and taking the square root, we find that the radius is approximately 7.00 units.

Tags

CCSS.7.G.B.4

Calculate the diameter of a circle with a circumference of 31.4 units. (Use π = 3.14)

• 5

• 10

• 20

• 15

Answer explanation

To calculate the diameter of a circle using its circumference, we can use the formula: Circumference = π × Diameter. Given the circumference is 31.4 units and π = 3.14, we can rearrange the formula to find the diameter: Diameter = Circumference ÷ π. Therefore, Diameter = 31.4 ÷ 3.14 = 10 units, which is the correct answer.

Tags

CCSS.7.G.B.4