To find the total volume of ice cream in the cone and on top, we first determine the volume of the hemisphere, which is given as 4 cubic inches. The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3} \pi r^2 h \), and since the diameter is equal to the height for the cone, we have \( r = \frac{h}{2} \). Setting \( h = d = 2r \), the volume can also be expressed as \( V = \frac{1}{3} \pi r^2 (2r) = \frac{2}{3} \pi r^3 \), and by equating this to the volume of the hemisphere and solving for \( r \), we find the total volume is \( 8 \) cubic inches (4 from the hemisphere plus the calculated volume of the cone).
Aimee packs ice cream into an ice cream cone. She then puts a perfect hemisphere of ice cream on top of the cone that has a volume of 4 in." The diameter of the ice cream cone is equal to its height. What is the total volume of ice cream in and on top of the cone? Use the relationship between the formulas for the volumes of cones and spheres to help solve this problem. Show your work and explain your reasoning. in 3 sentences
1 answer
1 answer