Question

Morgan has completed the mathematical statements shown below. Which statements are true regarding these formulas? Select *three* options.

--The numerical values of the area and circumference are equal when r=2
--The numerical value of the area is less than the numerical value of the circumference when r<2
--The numerical value of the area is greater than the numerical value of the circumference when r<2
--The numerical value of the area is less than the numerical value of the circumference when r>2
--The numerical value of the area is greater than the numerical value of the circumference when r>2

Answer 1

Answer:

• The numerical values of the area and circumference are equal when r=2
• The numerical value of the area is less than the numerical value of the circumference when r<2
• The numerical value of the area is greater than the numerical value of the circumference when r>2

Step-by-step explanation:

The formulas for area (A) and circumference (C) are ...

  A = πr² = (πr)r

  C = 2πr = (πr)2

Comparing numerical values, ...

when r=2, these have the same numerical value;

when r < 2, area is smaller;

when r > 2, area is larger.

Answer 2

The statements that are true regarding the formulas of area and circumference of  a circle are:

• The numerical values of the area and the circumference will be equal, when r = 2.
• The numerical value of the area is greater than that of the circumference, when r > 2.
• The numerical value of the area is less than that of the circumference, when r < 2.

Area and Circumference of a Circle

• The area is given as: πr².
• The circumference of a circle is: 2πr.

Thus, when r = 2,

Area = π(2²) = 4π

Circumference = 2π(2) = 4π

This implies that, the numerical values of the area and the circumference will be equal, when r = 2.

Thus, when r > 2, say r = 3, we have:

Area = π(3²) = 9π

Circumference = 2π(3) = 6π

This implies that, the numerical value of the area is greater than that of the circumference, when r > 2.

Thus, when r < 2, say r = 1, we have:

Area = π(1²) = π

Circumference = 2π(1) = 2π

This implies that, the numerical value of the area is less than that of the circumference, when r < 2.

In conclusion, the statements that are true regarding the formulas of area and circumference of  a circle are:

• The numerical values of the area and the circumference will be equal, when r = 2.
• The numerical value of the area is greater than that of the circumference, when r > 2.
• The numerical value of the area is less than that of the circumference, when r < 2.

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