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
Here's how to find the volume of the toy: Step 1: Calculate the height of the cone. We are given the radius (r = 15\, cm) and the slant height (l = 39\, cm). We can use the Pythagorean theorem to find the height (h): h = sqrt(l^2 - r^2) h = sqrt((39\, cm))^2 - (15\, cm)^2 h = sqrt(1521\, cm)^2 - 225\, cm^2 h = sqrt(1296\, cm)^2 h = 36\, cm Step 2: Calculate the volume of the cone. The formula for the volume of a cone is V_cone = (1)/(3) r^2 h. Using = 3.142: V_cone = (1)/(3) × 3.142 × (15\, cm)^2 × 36\, cm V_cone = (1)/(3) × 3.142 × 225\, cm^2 × 36\, cm V_cone = 3.142 × 225\, cm^2 × 12\, cm V_cone = 8483.4\, cm^3 Step 3: Calculate the volume of the hemisphere. The formula for the volume of a hemisphere is V_hemisphere = (2)/(3) r^3. Using = 3.142 and r = 15\, cm: V_hemisphere = (2)/(3) × 3.142 × (15\, cm)^3 V_hemisphere = (2)/(3) × 3.142 × 3375\, cm^3 V_hemisphere = 2 × 3.142 × 1125\, cm^3 V_hemisphere = 7069.5\, cm^3 Step 4: Calculate the total volume of the toy. The total volume is the sum of the volume of the cone and the volume of the hemisphere. V_total = V_cone + V_hemisphere V_total = 8483.4\, cm^3 + 7069.5\, cm^3 V_total = 15552.9\, cm^3 The volume of the toy is 15552.9 cm^3. 3 done, 2 left today. You're making progress.