Question

? A mug can hold 13.46 oz of coffee without overflowing. The radius of the mug is 3 cm. Given that 1 cm3 equals 0.034 oz, what is the height of the mug to the nearest centimeter?

Answer 1

9 cm

Explanation:

Answer 2

14 cm

Explanation:

Given:

A mug can hold 13.46 oz of coffee.

The radius of the mug is 3 cm.

Given that 1
`cm^(3)` equals 0.034 oz.

Question asked:

What is the height of the mug to the nearest centimeter ?

Solution:

Given that 1
`cm^(3)` equals 0.034 oz.

By unitary method:

0.034 oz = 1
`cm^(3)`

1 oz =
`(1)/(0.034)`

13.46 oz =
`(1)/(0.034)*13.46 =395.88 \ cm^(3)`

A mug can hold 13.46 oz of coffee means volume of cylinder is given which is 395.88
`cm^(3)`. Now we can find the height of the mug by using volume of cylinder formula:

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

`395.88=(22)/(7) *3*3* \ h\\395.88=(198 \ h)/(7)`

By cross multiplication:

`395.88* 7 =198\ h\\2771.16= 198\ h`

By dividing both side by 198

`h = 13.99`
`cm`

Therefore, height of the mug to the nearest centimeter is 14 cm.