(which means that the square pan is larger than the circular pan. so the square pan is 54.93824 in² larger than the circular pan.)
(why the answers is negative? since the question states "How much Larger is a Circular pan than the square pan. ." so the answer is negative coz it was asking for the circular pan and not the square pan. See the figure I made for you to visualize the "extra areas" which is in black / shaded part of the square pan.)
Answers & Comments
Answer:
Step-by-step explanation:
7. Area of the big square:
A₁ = s²
A₁ = (22)²
A₁ = 484 cm²
area of the small square
A₂ = s²
A₂ = 9²
A₂ = 81 cm²
Area of the shaded part:
A = A₁ - A₂
A = 484 - 81
A = 403 cm²
8 Area of a square:
A₁ = s²
A₁ = 24²
A₁ = 576 cm²
Area of a circle ( 2 semi-circles):
A₄ = πr²
r = 24/2 = 12cm
A₄ = π(12)² = 144π = 144(3.14159)
A₄ = 452.38896 cm²
or solving for each semi-circles:
1st semi-circle:
A₂ = (1/2)(πr²) = (1/2)[π(12)²] = (1/2)(144π)
A₂ = 72π = 72(3.14159) = 226.19448 cm²
2nd semi-circle:
A₃ = (1/2)(πr²) = (1/2)[π(12)²] = (1/2)(144π)
A₃ = 72π = 72(3.14159) = 226.19448 cm²
Area of 2 semi-circles:
A₄ = A₂ + A₃ = 226.19448 + 226.19448
A₄ = 452.38896 cm²
Total area of the shaded part:
A = A₁ - A₄ = 576 - 452.38896
A = 123.61104 cm²
9. let's divide the figure "I" into 3 rectangles.
Area of the 1st rectangle ( top ):
A₁ = lw = (6)(3) = 18 m²
Area of the 2nd rectangle ( middle ):
w= 6 -2 -2 = 2m
l = 4m
A₂ = lw = (4)(2) = 8 m²
Area of the 3rd/last rectangle ( bottom )
A₃ = lw = (6)(3) = 18 m²
Total Area of the figure "I":
A = A₁ + A₂ + A₃
A = 18 + 8 + 18
A = 44 m²
10. Area of a circular pan:
A₁ = πr²
r = 16/2 = 8 inches
A₁ = π(8)² = 64π = 64(3.14159)
A₁ = 201.06176 in²
Area of a square pan:
A₂ = s²
A₂ = 16²
A₂ = 256 in²
Total difference of both pans:
A = A₁ - A₂
A = 201.06176 - 256
A = -54.93824 in²
(which means that the square pan is larger than the circular pan. so the square pan is 54.93824 in² larger than the circular pan.)
(why the answers is negative? since the question states "How much Larger is a Circular pan than the square pan. ." so the answer is negative coz it was asking for the circular pan and not the square pan. See the figure I made for you to visualize the "extra areas" which is in black / shaded part of the square pan.)
thank you.