Question

How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.

8.8 cubic inches
10.1 cubic inches
14.7 cubic inches
22.3 cubic inches

Answer 1

C. 14.7 cubic inches

Explanation:

We are given two cups A and B resembling a cone and a cylinder respectively.

Cup A: The radius of the base circle = 1 inch and the height of the cone = 4 inch

Thus, the volume of the cone =
`(\pi r^(2)* h)/(3)`

i.e. Volume of the cone =
`(\pi 1^(2)* 4)/(3)`

i.e. Volume of the cone =
`(4\pi)/(3)`

i.e. Volume of the cone = 4.19
`inch^(3)`

The cup A holds 4.19 cubic inches of juice.

Cup B: The radius of the base circle = 1 inch and the height of the cylinder = 6 inch

So, the volume of the cylinder=
`\pi r^(2)* h`

i.e. Volume of the cylinder=
`\pi 1^(2)* 6`

i.e. Volume of the cylinder=
`6\pi`

i.e. Volume of the cylinder= 18.85
`inch^(3)`

Thus, cup B holds 18.85 cubic inches of juice.

So, the difference in the volume = 18.85 - 4.19 = 14.66
`inch^(3)`

Hence, cup B holds 14.66 cubic inches more juice than cup A.