Question

5 formula 0.5 points snoopy the dog is on a 11-foot long chain that is attached to the corner of a garage, as shown in the picture below. the chain does not allow him to go past either of the adjacent sides of the garage, thereby allowing him to roam all the space inside 3/4 of a circle. how much space does snoopy have to roam? use 3.14 for pi. round your answer to the nearest tenth, but do not include \sq ft\ or \ft^2\ with your response. answer

Explanation:

Step1: Recall the area formula of a circle

The area of a full circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle. Here, the length of the chain is the radius, so \( r = 11 \) feet.

Step2: Calculate the area of 3/4 of the circle

Since Snoopy can roam in 3/4 of a circle, we need to find 3/4 of the area of the full circle. First, calculate the area of the full circle with \( r = 11 \) and \( \pi = 3.14 \):
\( A_{\text{full}} = 3.14\times11^2 \)
\( 11^2 = 121 \), so \( A_{\text{full}} = 3.14\times121 = 379.94 \) square feet.

Then, find 3/4 of this area:
\( A_{\text{roam}}=\frac{3}{4}\times379.94 \)
\( \frac{3}{4}\times379.94 = 0.75\times379.94 = 284.955 \)

Step3: Round to the nearest tenth

Rounding 284.955 to the nearest tenth gives 285.0 (since the hundredth digit is 5, we round up the tenth digit).

Answer:

285.0