Find the distance around and the area of each figure. Round to the nearest tenth.
quarter circle:
5 inches
d = 6.28 * 5 *(90/360) = 7.9in.
A = 3.14 * 5^2(90/360) = 19.6in^2.
To find the distance around a quarter circle, also known as the quarter circumference, we need to know the radius (r) of the circle. In this case, the radius is given as 5 inches.
The formula for finding the distance around a circle (circumference) is C = 2πr, where π is a constant approximately equal to 3.14159.
For a quarter circle, we need to calculate one-fourth of the full circumference. So, the formula becomes:
C_quarter = (1/4) * 2πr
Plugging in the given radius (r = 5 inches) into the formula, we get:
C_quarter = (1/4) * 2 * 3.14159 * 5
Simplifying the equation, we have:
C_quarter = 1.5708 * 10
= 15.708 inches (rounded to the nearest tenth)
Therefore, the distance around the quarter circle is approximately 15.7 inches (rounded to the nearest tenth).
To find the area of a quarter circle, we use the formula A = (1/4) * πr^2, where A represents area.
So, with the given radius of 5 inches, we substitute it into the formula:
A_quarter = (1/4) * 3.14159 * (5)^2
Simplifying the equation, we have:
A_quarter = 0.7854 * 25
= 19.635 square inches (rounded to the nearest tenth)
Hence, the area of the quarter circle is approximately 19.6 square inches (rounded to the nearest tenth).