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 solid. The solid consists of a cone standing on a hemisphere. The radius of the hemisphere (r) is 1 cm. The radius of the cone (r) is equal to the radius of the hemisphere, so r = 1 cm. The height of the cone (h) is equal to its radius, so h = 1 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. Substitute the values r = 1 cm and h = 1 cm: V_cone = (1)/(3) (1 cm)^2 (1 cm) V_cone = (1)/(3) (1 cm^2) (1 cm) V_cone = (1)/(3) 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. Substitute the value r = 1 cm: V_hemisphere = (2)/(3) (1 cm)^3 V_hemisphere = (2)/(3) (1 cm^3) V_hemisphere = (2)/(3) cm^3 Step 4: Calculate the total volume of the solid. The total volume of the solid is the sum of the volume of the cone and the volume of the hemisphere. V_total = V_cone + V_hemisphere V_total = (1)/(3) cm^3 + (2)/(3) cm^3 V_total = ((1)/(3) + (2)/(3)) cm^3 V_total = (3)/(3) cm^3 V_total = 1 cm^3 V_total = cm^3 The volume of the solid in terms of is cm^3. Send me the next one 📸