Question

A small bottle of Dr.Pepper holds 31.2 cm^3 of the delicious drink. For a New Years Eve party, you need enough juice to fill 6 cone- shaped glasses that have a 4cm diameter and a 3 cm height. How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?​

Answer 1

Approximately 3 bottles are needed to buy to completely fill the 6 glasses you need

Solution:

Given that,

A small bottle of Dr.Pepper holds 31.2 cm^3 of the delicious drink

Therefore,

`Volume\ of\ small\ bottle\ of\ Dr.pepper = 31.2\ cm^3`

For a New Years Eve party, you need enough juice to fill 6 cone- shaped glasses that have a 4 cm diameter and a 3 cm height

Find the volume of cone

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

Where, r is the radius and h is the height

Diameter = 4 cm

Radius = 4/2 = 2 cm

Height = 3 cm

Therefore,

`V = (3.14 * 2^2 * 3)/(3)\\\\V = (3.14 * 12)/(3)\\\\V = (37.68)/(3)\\\\V = 12.56`

Thus, for 6 cone shaped glasses:

Volume of 6 cone shaped galsses = 12.56 x 6 = 75.36
`cm^3`

How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?​

`\text{Number of Dr.pepper bottles } = \frac{\text{Volume of 6 cone shaped galsses}}{\text{Volume of small bottle of dr pepper}}\\\\\text{Number of Dr.pepper bottles } = (75.36)/(31.2)\\\\\text{Number of Dr.pepper bottles } = 2.4153`

Thus approximately 3 bottles are needed to buy to completely fill the 6 glasses you need