Question

Lucy wants to put out 32 ounces of orange juice in her favorite cylindrical pitcher for her family brunch. The pitcher is 13 cm in height and has a radius of 3 cm. Will the orange juice fit? A) No, because the volume of the vase is approximately 489.84 cubic centimeters, which is equivalent to 16.56 fluid ounces. B) No, because the volume of the vase is approximately 367.38 cubic centimeters, which is equivalent to 12.42 fluid ounces. C) Yes, because the volume of the vase is approximately 1469.52 cubic centimeters, which is equivalent to 49.69 fluid ounces. D) Yes, because the volume of the vase is approximately 367.38 cubic centimeters, which is equivalent to 10864.71 fluid ounces.

Answer 1

`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13 \end{cases}\implies V=\pi (3)^2(13)\implies \stackrel{V=117\pi}{V\approx367.57~cm^3}`

now, a US gallon(128 oz), has 3785 cm³, so if there are 128 oz in 3785 cm³, how many ounces are there in 367.57 cm³?

`\bf \begin{array}{ccll} oz& cm^3\\ \cline{1-2} 128&3785\\ x&367.57 \end{array}\implies \cfrac{128}{x}=\cfrac{3785}{367.57}\implies \cfrac{128\cdot 367.57}{3785}=x\implies \stackrel{oz}{12.4}\approx x`

so her pitcher can only hold as much as 12.4 ounces of OJ, so those 32oz won't fit in it.