Answer: Therefore, the area of the paper that remains after cutting out two semicircles from the rectangular piece of paper is 83 cm².
Step-by-step explanation:
We have a rectangular piece of paper with a length of 24 cm and a width of 10 cm. Two semicircles are cut out from the paper.
To find the area of the paper that remains, we need to calculate the area of the rectangle and then subtract the areas of the two semicircles from it.
Step 1: Calculate the area of the rectangle.
The area of a rectangle is given by the formula: Area = length × width.
In this case, the length is 24 cm and the width is 10 cm.
So, the area of the rectangle is:
Area of rectangle = 24 cm × 10 cm = 240 cm²
Step 2: Calculate the area of one semicircle.
The formula for the area of a circle is: Area = πr², where π is approximately 3.14 and r is the radius of the circle.
In this case, the radius of each semicircle is half the width of the rectangle, which is 10 cm ÷ 2 = 5 cm.
So, the area of one semicircle is:
Area of one semicircle = (3.14) × (5 cm)² = 3.14 × 25 cm² = 78.5 cm² (rounded to the nearest tenth)
Step 3: Calculate the total area of the two semicircles.
Since we have two semicircles, we need to multiply the area of one semicircle by 2:
Total area of two semicircles = 2 × Area of one semicircle = 2 × 78.5 cm² = 157 cm² (rounded to the nearest whole number)
Step 4: Subtract the area of the two semicircles from the area of the rectangle.
Area of the paper that remains = Area of rectangle - Total area of two semicircles
Area of the paper that remains = 240 cm² - 157 cm² = 83 cm² (rounded to the nearest whole number)
Therefore, the area of the paper that remains after cutting out two semicircles from the rectangular piece of paper is 83 cm².
