Answer:
48.7 cube inches
Step-by-step explanation:
Let us assume that the ice cream filled the entire volume of the cone.
Diameter of cone = 4 inches
height of cone = 7 inches
diameter of a sphere of ice cream = 5 inches
Total amount of ice cream = volume of cone + volume of sphere
volume of cone = [tex]\frac{1}{3}[/tex][tex]\pi[/tex][tex]r^{2}[/tex]h
r = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{4}{2}[/tex] = 2 inches
volume of the cone = [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]2 ^{2}[/tex] x 7
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x 4 x 7
= 29.3333 cube inches
volume of sphere = [tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
r = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{5}{2}[/tex] = 2.5 inches
volume of sphere ice cream = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](\frac{5}{2} )^{3}[/tex]
= [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]\frac{125}{27}[/tex]
= 19.40 cube inches
So that,
Total amount of ice cream = 29.33 + 19.40
= 48.7 cube inches
