Question

Scott wants to buy fencing to place around a semicircular rock garden The diameter of the semicircle is 16 feet Using 3.14 for pi he calculates that he needs to buy abut 25.12 feet of fencing. The fencing is sold by the foot, so he plans to buy 26 feet of fencing. Explain why Scott's reasoning is incorrect and find the correct amount of fencing he should buy

Answer 1

The diameter of the semicircle is 16 feet.

He calculates that he needs to buy abut 25.12 feet of fencing.

To find amount of fencing we find the circumference of semicircle

Circumference of semicircle = $\frac{1}{2}\pi d+d$

Where d is the diameter of the circle

d= 16 given and value of pi is 3.14

Circumference of semicircle = $\frac{1}{2}*3.14*16+16$

=25.12 + 16 = 41.12 feet

Scott's calculation was wrong because he forgot to add the diameter d

Circumference of circle  is half way of circle plus the diameter of circle.

Correct amount of fencing = 41.12 feet