Questions: Find the circumference and area of the circle. Express answers in terms of π and then round to the nearest tenth. Find the circumference in terms of π C= (Type an exact answer in terms of π.) Find the circumference rounded to the nearest tenth. C= Find the area in terms of π A= (Type an exact answer in terms of π.) Find the area rounded to the nearest tenth. A=

Find the circumference and area of the circle. Express answers in terms of π and then round to the nearest tenth.

Find the circumference in terms of π
C=
(Type an exact answer in terms of π.)

Find the circumference rounded to the nearest tenth.
C=

Find the area in terms of π
A= (Type an exact answer in terms of π.)

Find the area rounded to the nearest tenth.
A=

Transcript text: Find the circumference and area of the circle. Express answers in terms of $\pi$ and then round to the nearest tenth. Find the circumference in terms of $\pi$ $C=$ $\square$ $\square$ (Type an exact answer in terms of $\pi$.) Find the circumference rounded to the nearest tenth. $C=$ $\square$ $\square$ Find the area in terms of $\pi$ $A=$ $\square$ (Type an exact answer in terms of $\pi$.) Find the area rounded to the nearest tenth. $A=$ $\square$ $\square$

Solution

Solution Steps

To solve this problem, we need to find both the circumference and the area of a circle given its radius. The formulas for these are:

Circumference in terms of $\pi$: $C = 2\pi r$
Area in terms of $\pi$: $A = \pi r^2$

We will then calculate the numerical values of these expressions by substituting the value of $\pi$ and rounding to the nearest tenth.

Step 1: Find the Circumference in Terms of $\pi$

The formula for the circumference $C$ of a circle is given by: \[ C = 2\pi r \] Substituting $r = 5$: \[ C = 2\pi \cdot 5 = 10\pi \]

Step 2: Find the Circumference Rounded to the Nearest Tenth

Using the value of $\pi \approx 3.1416$, we calculate the circumference: \[ C \approx 2 \cdot 3.1416 \cdot 5 \approx 31.4159 \] Rounding to the nearest tenth gives: \[ C \approx 31.4 \]

Step 3: Find the Area in Terms of $\pi$

The formula for the area $A$ of a circle is given by: \[ A = \pi r^2 \] Substituting $r = 5$: \[ A = \pi \cdot 5^2 = 25\pi \]

Step 4: Find the Area Rounded to the Nearest Tenth

Using the value of $\pi \approx 3.1416$, we calculate the area: \[ A \approx 3.1416 \cdot 25 \approx 78.54 \] Rounding to the nearest tenth gives: \[ A \approx 78.5 \]