Question 1·Easy·Geometry and Trigonometry

0 / 200

What is the area, in square inches, of a circle with a diameter of 18 inches? Express your answer in terms of $\pi$ .

For circle area, the cue is a diameter given but area requested. The formula $A=\pi r^2$ uses the radius $r$ , the distance from the center to the edge, so halve the diameter before squaring. Use Desmos to find the coefficient of $\pi$ , then leave $\pi$ in the exact answer. Squaring the diameter instead makes the area four times too large.

Hints

Hint 1
A diameter crosses the whole circle through its center, while a radius reaches only from the center to the edge. The radius is half the diameter. What length will you use in the area formula?
Hint 2
The area of a circle is $A=\pi r^2$ , where $r$ is its radius. Square the radius, not the diameter, and keep $\pi$ in your answer rather than replacing it with a decimal.

Step-by-step

Halve the diameter, then find the area
Step 1
Find the radius
A diameter crosses the center, while a radius runs from the center to the edge. Two radii make the given diameter, so halve the diameter before squaring:
$r=\frac{18}{2}=9\text{ inches}.$
Step 2
Put the radius in the area formula
Area is the space inside the circle, so use $A=\pi r^2$ with the radius, not the diameter. Substitute $r=9$ :
$A=\pi(9)^2.$
Step 3
Find the coefficient of pi
The answer must stay in terms of $\pi$ . Type $\frac{\pi(9)^2}{\pi}$ in Desmos to find the number multiplying $\pi$ ; it shows $81$ . So the circle's area is $81\pi$ square inches. Choice B.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreFind perimeter and area of plane figures

Question 1·Easy·Geometry and Trigonometry

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this