Question

find the circumference and area of the circle. express answers in terms of π and then round to the nearest hundredth.
find the circumference rounded to the nearest hundredth.
c =
(type an exact answer in terms of π.)
find the circumference rounded to the nearest hundredth.
c =
find the area in terms of π.
a =
(type an exact answer in terms of π.)
find the area rounded to the nearest hundredth.
a =

Explanation:

Step1: Recall circle - formulas

The formula for the circumference of a circle is $C = 2\pi r$ and the formula for the area of a circle is $A=\pi r^{2}$, where $r$ is the radius of the circle. Given the diameter $d = 40$ yd, the radius $r=\frac{d}{2}=20$ yd.

Step2: Calculate the exact - circumference

Using the formula $C = 2\pi r$, substitute $r = 20$ yd. So $C=2\pi(20)=40\pi$ yd.

Step3: Calculate the rounded - circumference

Take $\pi\approx3.14159$. Then $C = 40\pi\approx40\times3.14159 = 125.6636\approx125.66$ yd.

Step4: Calculate the exact - area

Using the formula $A=\pi r^{2}$, substitute $r = 20$ yd. So $A=\pi(20)^{2}=400\pi$ yd².

Step5: Calculate the rounded - area

Take $\pi\approx3.14159$. Then $A = 400\pi\approx400\times3.14159=1256.636\approx1256.64$ yd².

Answer:

$C = 40\pi$ yd, $C\approx125.66$ yd, $A = 400\pi$ yd², $A\approx1256.64$ yd²