Mathematics, 24.07.2020 09:01 lberries08
A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.) height cm radius cm
Answers: 1
) and the surface area (
) of the cone, measured in cubic centimeters and square centimeters, respectively, are modelled after these formulas:
- Height of the cylinder, measured in centimeters.
- Radius of the base of the cylinder, measured in centimeters.
, then: 
![A'_{s} = 31.258\cdot \left[\frac{\left(\frac{3\cdot h^{2}}{\sqrt{99+h^{2}}}\right)\cdot h - \sqrt{99+h^{3}} }{h^{2}}\right]](/tpl/images/0712/3564/9baab.png)
![A'_{s} = 31.258\cdot \left[2\cdot h\cdot (99+h^{2}})^{-0.5} -99\cdot h^{-2}\cdot (99+h^{2})^{-0.5}\right]](/tpl/images/0712/3564/92c32.png)
![A''_{s} = 31.258\cdot \left[(2+198\cdot h^{-3})\cdot (99+h)^{-0.5}-0.5\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-1.5}\right]](/tpl/images/0712/3564/dd943.png)
![h= \sqrt[3]{\frac{99}{2} }](/tpl/images/0712/3564/ded61.png)
![A''_{s} = 31.258\cdot \{[2+198\cdot (3.672)^{-3}]\cdot (99+3.672)^{-0.5}-0.5\cdot [2\cdot (3.672) - 99\cdot (3.672)^{-2}]\cdot (99+3.672)^{-1.5}\}](/tpl/images/0712/3564/98c1f.png)
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A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. Find the height and radius o...
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