Question

An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the volume of each drinking cup?

Answer 1

`Volume\approx 7.90 in^3`

to the nearest tenth

Step-by-step explanation

The given cup has the shape of a cone with dimension,

`height=4in.`

and

`diameter=2(3)/(4)in.`

The formula for calculating the area of a cone is given by;

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

Where r is the radius of the circular base.

We therefore divide the diameter in to two to find the radius.

This implies that,

`r=2(3)/(4) /2`

`r=(11)/(4) /2`

`r=(11)/(4) * (1)/(2)`

`r=(11)/(8)`

We now plug in all the above in to the formula, to get,

`Volume=(1)/(3) \pi ((11)/(8))^2*4`

`Volume=(121)/(48) \pi`

`Volume=7.918`

`Volume\approx 7.90 in^3`

to the nearest tenth

Answer 2

The volume of a cone is given by the formula
`V=(1)/(3) \pi r^(2) h`

If we plug in the known information into the formula, we will get the answer.

`d=2.75 in`

We know radius is half of d, so
`r=0.5*2.75=1.375 in`

The height is given as 4 in.

Pluggin all of these in the original formula gives us:

`V=(1)/(3) \pi (1.375)^(2) (4)=7.919 cubic inches`

Rounded to the nearest tenth, our final answer is:

V=7.9 cubic inches