This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to your geometry problems. Q1. Find the Area in the square but outside the circle The diagram shows a square with an inscribed circle. The side length of the square is 8 cm. This means the diameter of the circle is also 8 cm, so the radius of the circle is r = (8)/(2) = 4 cm. Step 1: Calculate the area of the square. The area of a square is given by A_square = side^2. A_square = (8 cm)^2 A_square = 64 cm^2 Step 2: Calculate the area of the circle. The area of a circle is given by A_circle = r^2. A_circle = (4 cm)^2 A_circle = 16 cm^2 Using ≈ 3.14159: A_circle ≈ 16 × 3.14159 cm^2 A_circle ≈ 50.265 cm^2 Step 3: Calculate the area in the square but outside the circle. This area is the difference between the area of the square and the area of the circle. A_difference = A_square - A_circle A_difference = 64 cm^2 - 16 cm^2 A_difference ≈ 64 cm^2 - 50.265 cm^2 A_difference ≈ 13.735 cm^2 Answer: 13.735 cm^2 (approx.) or (64 - 16) cm^2 Q2. Calculate the area and circumference of the circle shown below. use = 3.14 The diagram shows a circle with a radius (r) of 4.5 ft. Step 1: Calculate the area of the circle. The area of a circle is A = r^2. A = 3.14 × (4.5 ft)^2 A = 3.14 × 20.25 ft^2 A = 63.585 ft^2 Step 2: Calculate the circumference of the circle. The circumference of a circle is C = 2 r. C = 2 × 3.14 × 4.5 ft C = 6.28 × 4.5 ft C = 28.26 ft Answer: Area = 63.585 ft^2, Circumference = 28.26 ft Q3. Calculate the area and circumference of the circle shown below. use = 3.14 The diagram shows a circle with a diameter (d) of 14 in. The radius (r) is half of the diameter, so r = (14)/(2) = 7 in. Step 1: Calculate the area of the circle. The area of a circle is A = r^2. A = 3.14 × (7 in)^2 A = 3.14 × 49 in^2 A = 153.86 in^2 Step 2: Calculate the circumference of the circle. The circumference of a circle is C = d or C = 2 r. C = 3.14 × 14 in C = 43.96 in Answer: Area = 153.86 in^2, Circumference = 43.96 in Q4. Calculate the perimeter. Give your answer to 1 decimal place. The diagram shows a semicircle with a diameter (d) of 4 cm. The radius (r) is half of the diameter, so r = (4)/(2) = 2 cm. The perimeter of a semicircle includes the curved arc length and the straight diameter. Step 1: Calculate the length of the curved arc. The arc length of a semicircle is half the circumference of a full circle: (1)/(2) (2 r) = r. Arc\ Length = × 2 cm Arc\ Length = 2 cm Using ≈ 3.14159: Arc\ Length ≈ 2 × 3.14159 cm Arc\ Length ≈ 6.28318 cm Step 2: Calculate the total perimeter. The perimeter is the arc length plus the diameter. Perimeter = Arc\ Length + d Perimeter = 2 cm + 4 cm Perimeter ≈ 6.28318 cm + 4 cm Perimeter ≈ 10.28318 cm Step 3: Round the answer to 1 decimal place. Perimeter ≈ 10.3 cm Answer: 10.3 cm That's 2 down. 3 left today — send the next one.