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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You're on a roll — let's calculate the areas and radii for these circles! The formula for the area of a circle is A = r^2, where r is the radius. We will use = (22)/(7) as shown in the examples. 1. Calculate the area of a circle of radius 20cm. Step 1: Identify the given radius. r = 20 cm Step 2: Apply the area formula. A = r^2 A = (22)/(7) × (20 cm)^2 A = (22)/(7) × 400 cm^2 A = (8800)/(7) cm^2 Step 3: Calculate the numerical value. A ≈ 1257.14 cm^2 The area of the circle is 1257.14 cm^2. 2. Find the area of a circle whose diameter is 28cm. Step 1: Determine the radius from the given diameter. d = 28 cm r = (d)/(2) = 28 cm2 = 14 cm Step 2: Apply the area formula. A = r^2 A = (22)/(7) × (14 cm)^2 A = (22)/(7) × 196 cm^2 Step 3: Simplify the expression. A = 22 × 28 cm^2 A = 616 cm^2 The area of the circle is 616 cm^2. 3. The area of a circle whose is 145cm. Calculate its radius. (Assuming the question means "The area of a circle whose area is 145 cm^2") Step 1: Identify the given area. A = 145 cm^2 Step 2: Use the area formula to solve for the radius. A = r^2 145 cm^2 = (22)/(7) r^2 Step 3: Isolate r^2 and then solve for r. r^2 = (145 × 7)/(22) cm^2 r^2 = (1015)/(22) cm^2 r = sqrt((1015)/(22)) cm Step 4: Calculate the numerical value. r ≈ sqrt(46.136) cm r ≈ 6.79 cm The radius of the circle is 6.79 cm. 4. The diameter of the clock face on a town hall is 30cm. Find area of the clock face to the 1 cm. Step 1: Determine the radius from the given diameter. d = 30 cm r = (d)/(2) = 30 cm2 = 15 cm Step 2: Apply the area formula. A = r^2 A = (22)/(7) × (15 cm)^2 A = (22)/(7) × 225 cm^2 Step 3: Calculate the numerical value and round to the nearest whole number. A = (4950)/(7) cm^2 A ≈ 707.14 cm^2 Rounding to the nearest 1 cm^2: A ≈ 707 cm^2 The area of the clock face is 707 cm^2. 5. Find the area of the circular web of a spider if the radius is 1.4cm. Step 1: Identify the given radius. r = 1.4 cm Step 2: Apply the area formula. A = r^2 A = (22)/(7) × (1.4 cm)^2 A = (22)/(7) × 1.96 cm^2 Step 3: Simplify the expression. A = 22 × 0.28 cm^2 A = 6.16 cm^2 The area of the circular web is 6.16 cm^2. 6. What is the area of a circle of radius 3.5cm? Step 1: Identify the given radius. r = 3.5 cm Step 2: Apply the area formula. A = r^2 A = (22)/(7) × (3.5 cm)^2 A = (22)/(7) × ((7)/(2))^2 cm^2 Step 3: Simplify the expression. A = (22)/(7) × (49)/(4) cm^2 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. Drop the next question!