Question

Gerardo works at an ice cream shop each flavor of ice cream is stored in a right cylindrical tub that measures approximately 9 inches high with a radius of 5 inches Gerardo uses an ice cream scoop that makes spherical scoops of ice cream with a diameter of 2.5 inches If gerardo opens a new tub of chocolate ice cream and scoops 37 scoops of chocolate ice cream about how much chocolate ice cream in cubic inches is left in the tub

Answer 1

Volume left = 404.32 cubic inches

Explanation:

volume of a cylinder =
`\pi`
`r^(2)`h

volume of ice cream in the cylindrical tub =
`(22)/(7)` x
`5^(2)` x 9

=
`(22)/(7)` 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 =
`(4)/(3)`
`\pi`
`r^(3)`

r =
`(2.5)/(2)`

=
`(5)/(4)` inches

volume of the scoop =
`(4)/(3)` x
`(22)/(7)` x
`((5)/(4) )^(3)`

=
`(4)/(3)` x
`(22)/(7)` x
`(125)/(64)`

= 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.