A composite solid comprises a frustum of a cone mounted on a hemisphere. Calculate the volume of the solid correct to two decimal places.

Mohaa, let's knock this out. Question 18: A composite solid comprises a frustum of a cone mounted on a hemisphere. Given Information: Diameter of hemisphere = diameter of the bottom of the frustum = 30 cm. Entire solid has a vertical height of 60 cm. Radius of the top of the frustum = 10 cm. Use = (22)/(7). --- Part a) Calculate the volume of the solid correct to two decimal places. Step 1: Determine the dimensions of the hemisphere. The diameter of the hemisphere is 30 cm. The radius of the hemisphere (R_H) is half the diameter: R_H = (30)/(2) = 15 cm The height of the hemisphere is equal to its radius: h_H = 15 cm Step 2: Calculate the volume of the hemisphere. The formula for the volume of a hemisphere is V_H = (2)/(3) R_H^3. V_H = (2)/(3) × (22)/(7) × (15)^3 V_H = (2)/(3) × (22)/(7) × 3375 V_H = (44)/(21) × 3375 V_H = (148500)/(21) = (49500)/(7) cm^3 Step 3: Determine the dimensions of the frustum. The radius of the bottom of the frustum (R_B) is equal to the radius of the hemisphere: R_B = 15 cm The radius of the top of the frustum (R_T) is given as: R_T = 10 cm The total height of the solid is 60 cm. The height of the frustum (h_F) is the total height minus the height of the hemisphere: h_F = 60 - h_H = 60 - 15 = 45 cm Step 4: Calculate the volume of the frustum. The formula for the volume of a frustum is V_F = (1)/(3) h_F (R_B^2 + R_B R_T + R_T^2). V_F = (1)/(3) × (22)/(7) × 45 × (15^2 + 15 × 10 + 10^2) V_F = (1)/(3) × (22)/(7) × 45 × (225 + 150 + 100) V_F = (22)/(7) × 15 × (475) V_F = (330)/(7) × 475 V_F = (156750)/(7) cm^3 Step 5: Calculate the total volume of the solid. The total volume (V_total) is the sum of the volume of the hemisphere and the volume of the frustum. V_total = V_H + V_F V_total = (49500)/(7) + (156750)/(7) V_total = (49500 + 156750)/(7) V_total = (206250)/(7) V_total ≈ 29464.2857 cm^3 Rounding to two decimal places: V_total ≈ 29464.29 cm^3 --- Part b) The solid is melted and recast into cubes of side 16 cm. How many such cubes are realized? Step 1: Calculate the volume of one cube. The side of the cube (s) is 16 cm. The volume of one cube (V_cube) is s^3. V_cube = (16)^3 V_cube = 16 × 16 × 16 V_cube = 4096 cm^3 Step 2: Calculate the number of cubes. To find the number of cubes, divide the total volume of the solid by the volume of one cube. We use the exact value of the total volume for accuracy before rounding. Number of cubes = V_totalV_cube Number of cubes = (206250/7)/(4096) Number of cubes = (206250)/(7 × 4096) Number of cubes = (206250)/(28672) Number of cubes ≈ 7.1934 Since only whole cubes can be realized, we take the integer part of the result. Number of cubes = 7 Send me the next one 📸