![A bucket is 12cm in diameter at the top, 8cm in diameter at the bottom and 4cm deep. Calculate its volume in cm3 [JANB]](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1782933127532-76569bd1b48c087e.png&w=3840&q=75)
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
Step 1: Identify the given dimensions and convert diameters to radii. The bucket is a frustum of a cone. Top diameter (D_1) = 12 cm, so top radius (R_1) = (12)/(2) = 6 cm. Bottom diameter (D_2) = 8 cm, so bottom radius (R_2) = (8)/(2) = 4 cm. Depth (height, h) = 4 cm. Step 2: State the formula for the volume of a frustum of a cone. The volume V of a frustum of a cone is given by the formula: V = (1)/(3) h (R_1^2 + R_1 R_2 + R_2^2) Step 3: Substitute the values into the formula. Substitute h = 4 cm, R_1 = 6 cm, and R_2 = 4 cm into the formula: V = (1)/(3) (4) (6^2 + (6)(4) + 4^2) Step 4: Calculate the terms inside the parenthesis. V = (4)/(3) (36 + 24 + 16) V = (4)/(3) (76) Step 5: Calculate the final volume. V = (304)/(3) cm^3 Using ≈ 3.14159: V ≈ (304)/(3) × 3.14159 V ≈ 101.333 × 3.14159 V ≈ 318.90 cm^3 The volume of the bucket is (304)/(3) cm^3 ≈ 318.90 cm^3. That's 2 down. 3 left today — send the next one.