Find the volume specified. Use 3.14 as the approximate value of pie, and round your answer to the nearest tenth.
Find the volume of an ice cream cone (right circular cone) of radius 7 cm and height 9 cm topped by a perfect hemisphere of ice cream of the same radius.
To find the volume of the ice cream cone, we first need to find the volume of the cone and then add the volume of the hemisphere on top.
Volume of the cone:
V_cone = (1/3) * π * r^2 * h
V_cone = (1/3) * 3.14 * 7^2 * 9
V_cone ≈ 538.083 cm³
Volume of the hemisphere:
V_hemisphere = (2/3) * π * r^3
V_hemisphere = (2/3) * 3.14 * 7^3
V_hemisphere ≈ 705.304 cm³
Total volume:
V_total = V_cone + V_hemisphere
V_total ≈ 538.083 + 705.304
V_total ≈ 1243.387 cm³
Rounded to the nearest tenth, the volume of the ice cream cone is approximately 1243.4 cm³.