Question

A semicircle is cut out of a rectangular paperboard measuring 27 in long and 20 in wide, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? Do not round any intermediate computations. Round your final answer to the nearest hundredth and be sure to include the correct unit. If necessary, refer to the list of geometry formulas. Use the pi symbol. Options: A) 90.25 in B) 87.12 in C) 83.91 in D) 80.70 in

Answer 1

The perimeter of the paper board that will be remaining after the semicircle is removed is calculated as: 105.40 in. (None of the options is correct).

What is the perimeter of a semicircle?

The perimeter of the paper board that remains can be calculated by adding two lengths and a width of the rectangular paperboard together with the circumference of the semicircle which excludes its diameter.

Thus, the formula would be:

Perimeter of paperboard that remains = 2L + W + πr, where:

Length (L) = 27 in.

Width of rectangle (W) = 20 in.

π = 3.14 or 22/7

radius of the semicircle (r) = 1/2(20) = 10 in.

Plug in the values:

Perimeter of paperboard that remains = 2(27) + 20 + (3.14)(10)

Perimeter of paperboard that remains = 105.40 in.

None of the options given is correct.