Question

A drumstick ice cream cone is 4 inches in diameter and has a height of 7 inches and filled with ice cream. The cone also has a sphere of ice cream that's 5 inches in diameter on top. What is the total amount of ice cream? Round to the nearest tenth.

Answer 1

48.7 cube inches

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 =
`(1)/(3)`
`\pi`
`r^(2)`h

r =
`(diameter)/(2)`

=
`(4)/(2)` = 2 inches

volume of the cone =
`(1)/(3)` x
`(22)/(7)` x
`2 ^(2)` x 7

=
`(1)/(3)` x
`(22)/(7)` x 4 x 7

= 29.3333 cube inches

volume of sphere =
`(4)/(3)`
`\pi`
`r^(3)`

r =
`(diameter)/(2)`

=
`(5)/(2)` = 2.5 inches

volume of sphere ice cream =
`(4)/(3)` x
`(22)/(7)` x
`((5)/(2) )^(3)`

=
`(4)/(3)` x
`(22)/(7)` x
`(125)/(27)`

= 19.40 cube inches

So that,

Total amount of ice cream = 29.33 + 19.40

= 48.7 cube inches