Match each circle-related calculation on the left to its correct numerical value on the ri… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each circle-related calculation on the left to its correct numerical value on the right.

Area of a circle with a radius of $5$ $25\pi$
Circumference of a circle with a diameter of $10$ $10\pi$
Radius of a circle with an area of $100\pi$ $10$
Diameter of a circle with a circumference of $12\pi$ $12$

Answer

Area with radius 5 matches to 25π; Circumference with diameter 10 matches to 10π; Radius of area 100π matches to 10; Diameter of circumference 12π matches to 12.

Each match is verified by accurately applying the formulas

A = \pi r^2

and

C = \pi d

to either solve for the resulting property or to work backwards to find the missing dimension.

Step-by-Step Solution

Calculate the area for the first description.

Area =

25\pi

The formula for the area of a circle is

A = \pi r^2

. Substituting

r = 5

yields

25\pi

Calculate the circumference for the second description.

Circumference =

10\pi

The formula for circumference is

C = \pi d

. Substituting

d = 10

yields

10\pi

Solve for the radius in the third description.

Radius =

10

Given area

A = 100\pi

, use

100\pi = \pi r^2

to find that

r^2 = 100

, so

r = 10

Solve for the diameter in the fourth description.

Diameter =

12

Given circumference

C = 12\pi

, use

12\pi = \pi d

to determine that

d = 12

Key Concept

Calculating area, circumference, radius, and diameter of a circle using fundamental geometry formulas.

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