QuestionFind the area of a circle inscribing an 18-inch by 24-inch rectangle in square inches. Options: (A) , (B) , (C) , (D) .
Studdy Solution
STEP 1
Assumptions1. The rectangle is inscribed in the circle, which means the diameter of the circle is the diagonal of the rectangle.
. The dimensions of the rectangle are18 inches by24 inches.
3. We are asked to find the area of the circle.
STEP 2
First, we need to find the diagonal of the rectangle, which is the diameter of the circle. We can use the Pythagorean theorem for this, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the sides of the rectangle are the two sides of the right triangle.
STEP 3
Now, plug in the given values for the length and width of the rectangle to calculate the diameter.
STEP 4
Calculate the square of the diameter.
STEP 5
Take the square root of both sides to find the diameter.
STEP 6
Now that we have the diameter, we can find the radius of the circle by dividing the diameter by2.
STEP 7
Plug in the value for the diameter to calculate the radius.
STEP 8
Now that we have the radius, we can find the area of the circle using the formula for the area of a circle, which is .
STEP 9
Plug in the value for the radius to calculate the area.
STEP 10
Calculate the area of the circle.
So, the area of the circle is square inches. The correct answer is () .
Was this helpful?