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
The image contains several questions. I will solve question 9.B, which asks to calculate the volume of the frustum of a cone. The frustum has: • Top diameter = 6 cm • Bottom diameter = 18 cm • Height = 10 cm • Use = 3.142 Step 1: Identify the radii of the top and bottom bases. The radius is half of the diameter. r_1 = 6 cm2 = 3 cm r_2 = 18 cm2 = 9 cm The height of the frustum is h = 10 cm. Step 2: Use the formula for the volume of a frustum of a cone. The formula for the volume of a frustum of a cone is: V = (1)/(3) h (r_1^2 + r_1 r_2 + r_2^2) where h is the height, r_1 is the radius of the top base, and r_2 is the radius of the bottom base. Step 3: Substitute the given values into the formula. V = (1)/(3) × 3.142 × 10 cm × ((3 cm)^2 + (3 cm)(9 cm) + (9 cm)^2) Step 4: Calculate the terms inside the parenthesis. V = (1)/(3) × 3.142 × 10 cm × (9 cm^2 + 27 cm^2 + 81 cm^2) V = (1)/(3) × 3.142 × 10 cm × (117 cm^2) Step 5: Perform the multiplication to find the volume. V = (1)/(3) × 3.142 × 1170 cm^3 V = 3.142 × 390 cm^3 V = 1225.38 cm^3 The volume of the frustum is 1225.38 cm^3. Send me the next one 📸