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 dimensions of the cuboid. The cuboid has a length (L) of 10 cm, a width (W) of 8 cm, and a height (H) of 2 cm. Step 2: Calculate the volume of the cuboid. The formula for the volume of a cuboid is V_cuboid = L × W × H. V_cuboid = 10 cm × 8 cm × 2 cm V_cuboid = 160 cm^3 Step 3: Identify the dimensions of the cylinder. The cylinder has a diameter of 2.0 cm, which means its radius (r) is 2.0 cm2 = 1.0 cm. The height (h) of the cylinder is 3 cm. Step 4: Calculate the volume of the cylinder. The formula for the volume of a cylinder is V_cylinder = r^2 h. V_cylinder = (1.0 cm)^2 (3 cm) V_cylinder = (1 cm^2) (3 cm) V_cylinder = 3 cm^3 Using ≈ 3.14159: V_cylinder ≈ 3 × 3.14159 cm^3 V_cylinder ≈ 9.42477 cm^3 Step 5: Calculate the total volume of the composite shape. The total volume is the sum of the volume of the cuboid and the volume of the cylinder. V_total = V_cuboid + V_cylinder V_total = 160 cm^3 + 9.42477 cm^3 V_total = 169.42477 cm^3 Step 6: Convert the total volume from cubic centimeters to cubic meters. We know that 1 m = 100 cm. Therefore, 1 m^3 = (100 cm)^3 = 1,000,000 cm^3. To convert cm^3 to m^3, we divide by 1,000,000. V_total in m^3 = 169.42477 cm^31,000,000 cm^3/m^3 V_total in m^3 ≈ 0.00016942477 m^3 Rounding to three significant figures: V_total ≈ 0.000169 m^3 The volume of the shape is 0.000169 m^3. Send me the next one 📸