Question

A brand new gymnasium needs a circle with a diameter of 6 ft painted in the center of the wood floor. It must be marked with tape before it is painted. Use pialmost equals3.14.
​(a) How long will the tape​ be?
​(b) The circle is then painted. How large an area must be​ painted?
Question content area bottom
Part 1
​(a) The tape should be
  
enter your response here
▼
ft
ft squared
long.
​(Type a whole number or a decimal rounded to the nearest hundredth as​ needed.)

Answer 1

To solve this problem, let's start with the circle's characteristics.

### (a) Length of the Tape (Circumference of the Circle)

The formula for the circumference \( C \) of a circle is given by:

\[
C = \pi d
\]

where \( d \) is the diameter of the circle. We are given that the diameter \( d \) is 6 ft.

Using \( \pi \approx 3.14 \):

\[
C = 3.14 \times 6 = 18.84 \text{ ft}
\]

So, the length of the tape should be **18.84 ft**.

### (b) Area to be Painted

The formula for the area \( A \) of a circle is given by:

\[
A = \pi r^2
\]

where \( r \) is the radius of the circle. The radius \( r \) is half of the diameter:

\[
r = \frac{d}{2} = \frac{6}{2} = 3 \text{ ft}
\]

Now substituting the radius into the area formula:

\[
A = 3.14 \times (3)^2 = 3.14 \times 9 = 28.26 \text{ ft}^2
\]

So, the area that must be painted should be **28.26 ft²**.

### Summary

- (a) The tape should be **18.84 ft** long.
- (b) The area that must be painted is **28.26 ft²**.