A brand new gymnasium needs a circle with a diameter of 12 ft painted in the center of the wood floor. It must be marked with tape before it is painted. Use pialmost equals3.14.

Question

​(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.)
Part 2
​(b) In order to paint the​ circle, an area of
  
enter your response here
▼
ft squared
ft
must be painted.
​(Type a whole number or a decimal rounded to the nearest hundredth as​ needed.)

Answer 1

To solve the problem, we need to find the circumference of the circle (for the tape length) and the area of the circle (for the painting area).

Part 1: Length of the Tape

The diameter of the circle is given as 12 ft. The formula for the circumference \(C\) of a circle is:

\[ C = \pi \times d \]

where \(d\) is the diameter. With \(d = 12\) ft and using \(\pi \approx 3.14\):

\[ C = 3.14 \times 12 = 37.68 \text{ ft} \]

So, the tape should be 37.68 ft long.

Part 2: Area to be Painted

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

\[ A = \pi \times r^2 \]

where \(r\) is the radius of the circle. Since the diameter is 12 ft, the radius \(r\) is:

\[ r = \frac{d}{2} = \frac{12}{2} = 6 \text{ ft} \]

Now we can calculate the area:

\[ A = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \text{ ft}^2 \]

So, the area that must be painted is 113.04 ft².

Final Answers

• (a) The tape should be 37.68 ft long.
• (b) In order to paint the circle, an area of 113.04 ft² must be painted.