anonymous
  • anonymous
english question
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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mathstudent55
  • mathstudent55
First let's just summarize all the info we are given: One ice cream cone uses 1 scoop of sprinkles. In one day, 65 cones are sold. Silly Scoops is open every day of the month. A month has 30 days. A scoop has 88 sprinkles. Each sprinkle is a cylinder with 25 mm length and 2 mm radius. The density of a sprinkle is 2.2 g/ml
mathstudent55
  • mathstudent55
|dw:1371389807527:dw|
mathstudent55
  • mathstudent55
The conversion factor of cm to mm is 10 mm/1 cm or 1 cm/10 mm

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mathstudent55
  • mathstudent55
When you deal with a cubic unit for volume, then the conversion has to be cubed. (10 mm)^3/(1 cm)^2 = (1000 mm^3)/(1 cm ^3)
mathstudent55
  • mathstudent55
Since the dimensions of each sprinkle are given in mm, when you calculate the volume of a sprinkle, you are calculating in mm^3. The density of the sprinkle is given in g/ml. 1 ml = cm^3. So the density of the sprinkles is in g/cm^3, but we calculated the volume in mm^3, so we need to convert mm^3 to cm^3 to be able to use the given density.
mathstudent55
  • mathstudent55
yes
mathstudent55
  • mathstudent55
|dw:1371390883342:dw|
mathstudent55
  • mathstudent55
Correct. Both the numerator and denominator were raised to the 3rd power. That's why 1 cm/10 mm became (1 cm)^3 / (10 mm)^3
UnkleRhaukus
  • UnkleRhaukus
\[1 [\text{cm}]=10[\text{mm}]\\\frac{1 [\text{cm}]}{10[\text{mm}]}=1\\\left(\frac{1 [\text{cm}]}{10[\text{mm}]}\right)^3=1^3\\ \frac{1 [\text{cm}]^3}{10^3[\text{mm}]^3}=1\]
mathstudent55
  • mathstudent55
|dw:1371391303447:dw|
mathstudent55
  • mathstudent55
Every dimension you are given has 2 significant digits (88 sprinkles, 2.0 mm, 25 mm, 2.2 g/ml, etc.) except for the number of days in a month which has 1. Then again, the numbers of days in a month can be considered a fixed conversion factor, so it should not influence the result. So I'd go with 2 significant digits.
mathstudent55
  • mathstudent55
I get 261.4713424 lb
mathstudent55
  • mathstudent55
Yes, but like I wrote above, I'd go with 2 sf.
mathstudent55
  • mathstudent55
BTW, the conversion from grams to pounds I used above is exact.
mathstudent55
  • mathstudent55
Yes, 260 lb
mathstudent55
  • mathstudent55
I can't do it now. I have to go. I'll be glad to help when I get back. Post it in a new post and I'll look for it later.

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