Respuesta :
Answer:
14 cm
Step-by-step explanation:
Given:
A mug can hold 13.46 oz of coffee.
The radius of the mug is 3 cm.
Given that 1 [tex]cm^{3}[/tex] equals 0.034 oz.
Question asked:
What is the height of the mug to the nearest centimeter ?
Solution:
Given that 1 [tex]cm^{3}[/tex] equals 0.034 oz.
By unitary method:
0.034 oz = 1 [tex]cm^{3}[/tex]
1 oz = [tex]\frac{1}{0.034}[/tex]
13.46 oz = [tex]\frac{1}{0.034}\times13.46 =395.88 \ cm^{3}[/tex]
A mug can hold 13.46 oz of coffee means volume of cylinder is given which is 395.88 [tex]cm^{3}[/tex]. Now we can find the height of the mug by using volume of cylinder formula:
volume of cylinder = [tex]\pi r^{2} h[/tex]
[tex]395.88=\frac{22}{7} \times3\times3\times \ h\\395.88=\frac{198 \ h}{7}[/tex]
By cross multiplication:
[tex]395.88\times 7 =198\ h\\2771.16= 198\ h[/tex]
By dividing both side by 198
[tex]h = 13.99[/tex] [tex]cm[/tex]
Therefore, height of the mug to the nearest centimeter is 14 cm.
