ctangular piece of paper with length 38cm and width 18cm has two semicircles cut out of it, as shown below.Find the area of the paper that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit
Question
ctangular piece of paper with length 38cm and width 18cm has two semicircles cut out of it, as shown below.Find the area of the paper that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit
Solution
To find the area of the paper that remains, we first need to find the area of the rectangle and then subtract the area of the two semicircles.
Step 1: Find the area of the rectangle The area of a rectangle is given by the formula length × width. So, the area of the rectangle is 38cm × 18cm = 684 square cm.
Step 2: Find the area of the two semicircles The diameter of each semicircle is the width of the rectangle, which is 18cm. So, the radius of each semicircle is 18cm ÷ 2 = 9cm. The area of a circle is given by the formula πr². So, the area of each semicircle is 1/2 × π × (9cm)² = 1/2 × 3.14 × 81cm² = 127.26 square cm. Since there are two semicircles, their total area is 2 × 127.26 square cm = 254.52 square cm.
Step 3: Subtract the area of the semicircles from the area of the rectangle The area of the paper that remains is the area of the rectangle minus the area of the two semicircles, which is 684 square cm - 254.52 square cm = 429.48 square cm.
So, the area of the paper that remains is 429.48 square cm.
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