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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Let's continue with these circle problems! We'll use the formula for the area of a circle A = r^2 and = (22)/(7). 7. What is the area of a circle if the diameter is 7cm? Step 1: Determine the radius from the given diameter. d = 7 cm r = (d)/(2) = (7)/(2) cm Step 2: Apply the area formula. A = r^2 A = (22)/(7) × ((7)/(2) cm)^2 A = (22)/(7) × (49)/(4) cm^2 Step 3: Simplify the expression. A = (22 × 7)/(4) cm^2 A = (154)/(4) cm^2 A = 38.5 cm^2 The area of the circle is 38.5 cm^2. 8. The area of a circle is 2464cm^2. Calculate its diameter to 2 sig. figures. Step 1: Identify the given area and use the area formula to find the radius. A = 2464 cm^2 A = r^2 2464 cm^2 = (22)/(7) r^2 Step 2: Solve for r^2 and then r. r^2 = (2464 × 7)/(22) cm^2 r^2 = (17248)/(22) cm^2 r^2 = 784 cm^2 r = sqrt(784) cm r = 28 cm Step 3: Calculate the diameter. d = 2r d = 2 × 28 cm d = 56 cm Step 4: Express the diameter to 2 significant figures. The diameter is already 56 cm, which has two significant figures. The diameter of the circle is 56 cm. 9. Find the area of a semi circular field of diameter 20m. Step 1: Determine the radius from the given diameter. d = 20 m r = (d)/(2) = 20 m2 = 10 m Step 2: Apply the formula for the area of a semi-circle. The area of a semi-circle is half the area of a full circle. A_semi = (1)/(2) r^2 A_semi = (1)/(2) × (22)/(7) × (10 m)^2 A_semi = (1)/(2) × (22)/(7) × 100 m^2 Step 3: Simplify the expression. A_semi = (11)/(7) × 100 m^2 A_semi = (1100)/(7) m^2 A_semi ≈ 157.14 m^2 The area of the semi-circular field is 157.14 m^2. 10. What is the diameter of a circle whose area is 154cm^2? Step 1: Identify the given area and use the area formula to find the radius. A = 154 cm^2 A = r^2 154 cm^2 = (22)/(7) r^2 Step 2: Solve for r^2 and then r. r^2 = (154 × 7)/(22) cm^2 r^2 = (1078)/(22) cm^2 r^2 = 49 cm^2 r = sqrt(49) cm r = 7 cm Step 3: Calculate the diameter. d = 2r d = 2 × 7 cm d = 14 cm The diameter of the circle is 14 cm. Last free one today — make it count tomorrow, or type /upgrade for unlimited.