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.
ScanSolve AI Answer
Alright Gomolemo — let's do this. Question 5: The area of a semi-circle is 5024 cm^2. a) Calculate the length of the straight lined side. The straight lined side of a semi-circle is its diameter. Step 1: Use the formula for the area of a semi-circle to find the radius r. Area = (1)/(2) r^2 5024 = (1)/(2) r^2 10048 = r^2 r^2 = (10048)/() r = sqrt((10048)/()) r ≈ sqrt((10048)/(3.1415926535)) r ≈ sqrt(3200.0000000000004) r ≈ 56.5685 cm Step 2: Calculate the length of the straight lined side (diameter). Diameter = 2r Diameter ≈ 2 × 56.5685 cm Diameter ≈ 113.137 cm Rounding to two decimal places: Diameter ≈ 113.14 cm The length of the straight lined side is 113.14 cm. b) What is the circumference of the semi-circle? Give your answer to the nearest centimetre. The circumference of a semi-circle includes the curved arc and the straight diameter. Step 1: Use the formula for the circumference of a semi-circle. Circumference = r + 2r Circumference = r( + 2) Using the calculated value of r ≈ 56.5685 cm: Circumference ≈ 56.5685 × (3.1415926535 + 2) Circumference ≈ 56.5685 × 5.1415926535 Circumference ≈ 290.999 cm Step 2: Round the circumference to the nearest centimetre. Circumference ≈ 291 cm The circumference of the semi-circle is 291 cm. Question 6: a) The area of a netball court is 465.125 m^2. If the breadth of the court is 15.25 m, what is the length? Step 1: Use the formula for the area of a rectangle. Area = Length × Breadth Step 2: Substitute the given values and solve for Length. 465.125 m^2 = Length × 15.25 m Length = 465.125 m^215.25 m Length = 30.5 m The length of the court is 30.5 m. b) A netball court is divided into thirds. What will the area of a third be? Give your answer to the nearest square metre. Step 1: Calculate the area of one third of the court. Area of one third = (1)/(3) × Total Area Area of one third = (1)/(3) × 465.125 m^2 Area of one third = 155.04166... m^2 Step 2: Round the area to the nearest square metre. Area of one third ≈ 155 m^2 The area of a third of the court is 155 m^2. Send me the next one 📸