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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Okay, scoddyevarau87@gmail.com, let's tackle these problems. Problem 24: Two triangles are similar with sides in the ratio 4:9. If the area of the smaller triangle is 64 cm^2, find the area of the larger triangle. Step 1: Understand the relationship between the ratio of sides and the ratio of areas for similar triangles. If the ratio of corresponding sides of two similar triangles is a:b, then the ratio of their areas is a^2:b^2. Given ratio of sides (smaller to larger) is 4:9. So, the ratio of their areas (smaller to larger) is 4^2:9^2 = 16:81. Step 2: Set up a proportion using the given area. Let A_S be the area of the smaller triangle and A_L be the area of the larger triangle. (A_S)/(A_L) = (16)/(81) We are given A_S = 64 cm^2. 64 cm^2A_L = (16)/(81) Step 3: Solve for A_L. A_L = 64 cm^2 × 8116 A_L = 4 cm^2 × 81 A_L = 324 cm^2 Problem 25: Define the term circle and state the relationship between radius and diameter. A circle is a set of all points in a plane that are equidistant from a fixed point called the center. The radius (r) is the distance from the center to any point on the circle. The diameter (D) is the distance across the circle passing through its center. The relationship is that the diameter is twice the radius, or D = 2r. Problem 26: Find the circumference of a Circle with a radius of 7 cm. ( = (22)/(7)) Step 1: Write the formula for the circumference of a circle. C = 2 r Step 2: Substitute the given values. Given r = 7 cm and = (22)/(7). C = 2 × (22)/(7) × 7 cm Step 3: Calculate the circumference. C = 2 × 22 cm C = 44 cm Problem 27: Calculate the area of the following use = (22)/(7). a) Circle with diameter 14 cm. Step 1: Find the radius. The diameter D = 14 cm, so the radius r = (D)/(2) = 14 cm2 = 7 cm. Step 2: Write the formula for the area of a circle. A = r^2 Step 3: Substitute the values and calculate. A = (22)/(7) × (7 cm)^2 A = (22)/(7) × 49 cm^2 A = 22 × 7 cm^2 A = 154 cm^2 b) Circle with diameter 12 cm. Step 1: Find the radius. The diameter D = 12 cm, so the radius r = (D)/(2) = 12 cm2 = 6 cm. Step 2: Write the formula for the area of a circle. A = r^2 Step 3: Substitute the values and calculate. A = (22)/(7) × (6 cm)^2 A = (22)/(7) × 36 cm^2 A = (792)/(7) cm^2 A ≈ 113.14 cm^2 c) Quadrant of a circle with radius 10 cm. Step 1: Write the formula for the area of a quadrant (quarter circle). A = (1)/(4) r^2 Step 2: Substitute the values. Given r = 10 cm and = (22)/(7). A = (1)/(4) × (22)/(7) × (10 cm)^2 A = (1)/(4) × (22)/(7) × 100 cm^2 Step 3: Calculate the area. A = (2200)/(28) cm^2 A = (550)/(7) cm^2 A ≈ 78.57 cm^2 Problem 28: The wheel of a bicycle has a radius of 35 cm. How many revolutions will it make in covering 1 km? Step 1: Calculate the circumference of the wheel. The circumference is the distance covered in one revolution. Use = (22)/(7). C = 2 r C = 2 × (22)/(7) × 35 cm C = 2 × 22 × 5 cm C = 220 cm Step 2: Convert the total distance to the same units as the circumference. Given total distance D_total = 1 km. 1 km = 1000 m 1000 m = 1000 × 100 cm = 100000 cm Step 3: Calculate the number of revolutions. Number of revolutions = D_totalC Number of revolutions = 100000 cm220 cm Number of revolutions = (10000)/(22) Number of revolutions = (5000)/(11) Number of revolutions ≈ 454.55 revolutions That's 2 down. 3 left today — send the next one.