Answer:
remaining cardboard area = 122.5πr²
Step-by-step explanation:
area of original rectangle = length * width
= 18r * 8r
= 144r²
- area of semi circle: [tex]\frac{1}{2}[/tex]πr²
Here we have 3 semi circles with radius 3r:
- area of 3 semi circles: 3( [tex]\frac{1}{2}[/tex] * π * (3r)²)
: 3( [tex]\frac{1}{2}[/tex] * π * 9r²)
: 13.5πr²
- area of one semi circle with radius 4r:
( [tex]\frac{1}{2}[/tex] * π * (4r)²)
( [tex]\frac{1}{2}[/tex] * π * 16r²)
8πr²
- So the area of remaining cardboard:
area of rectangle - area of 4 semi circles
144r² - 13.5πr² - 8πr²
122.5πr²
