Answer:
Volume left = 404.32 cubic inches
Step-by-step explanation:
volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
volume of ice cream in the cylindrical tub = [tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex] x 9
= [tex]\frac{22}{7}[/tex] x 25 x 9
= 707.1429
Volume of ice cream in the cylindrical tub is 707.14 cubic inches.
The ice cream scoop has a spherical volume, so that;
volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
r = [tex]\frac{2.5}{2}[/tex]
= [tex]\frac{5}{4}[/tex] inches
volume of the scoop = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](\frac{5}{4} )^{3}[/tex]
= [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]\frac{125}{64}[/tex]
= 8.1845
volume of the scoop is 8.19 cubic inches.
If he scoops 37 scoops,
volume of the 37 scoops = 37 x 8.1845
= 302.8265
volume of 37 scoops is 302.83 cubic inches.
Volume of ice cream left in the tub = 707.1429 - 302.8265
= 404.3164
Volume of ice cream left in the tub is 404.32 cubic inches.
