At a neutrino detection facility deep underground in an abandoned salt mine, a research team is making calculationson how muchof two materials they will need in order to line the inside of adetection tank. The detection tank is a large sphere with an interior radius of 45.55 ft±0.500in. The two materials needed are gold with a density of 19.33 g/cm3and titanium with a density of 0.1630 lbs/in3. On the interior, the titanium layer will be applied first and the gold on top of that. The researchers look to purchaseenough titaniumto apply a layer that covers the entire interior of the sphere and has a thickness of 1.335 cm±0.500cm. Theprice of titaniumis $29.00per kg. On top of the titanium, the researches need to apply a layer of gold that is 700.0 microns thick and coversthe entire interior of the tank. The price of gold is $2,035per oz. What is the percent error in your calculation of gold needed if you ignored the change in volume to the tank created by applying the titanium layer first? Is the difference in mass between the amount of gold required when the change in volume to the tank created by applying the titanium layer first is taken into account versus when it is ignored actually statistically significant? Show numerically. How much total money in dollars will the researches need to spend in order to be sure they cover apply layers with the desired thicknesses but potentially have no material left over?
At a neutrino detection facility deep underground in an abandoned salt mine, a research team is making calculationson how muchof two materials they will need in order to line the inside of adetection tank. The detection tank is a large sphere with an interior radius of 45.55 ft±0.500in. The two materials needed are gold with a density of 19.33 g/cm3and titanium with a density of 0.1630 lbs/in3. On the interior, the titanium layer will be applied first and the gold on top of that.
The researchers look to purchaseenough titaniumto apply a layer that covers the entire interior of the sphere and has a thickness of 1.335 cm±0.500cm. Theprice of titaniumis $29.00per kg. On top of the titanium, the researches need to apply a layer of gold that is 700.0 microns thick and coversthe entire interior of the tank. The price of gold is $2,035per oz.
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What is the percent error in your calculation of gold needed if you ignored the change in volume to the tank created by applying the titanium layer first?
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Is the difference in mass between the amount of gold required when the change in volume to the tank created by applying the titanium layer first is taken into account versus when it is ignored actually statistically significant? Show numerically.
- How much total money in dollars will the researches need to spend in order to be sure they cover apply layers with the desired thicknesses but potentially have no material left over?
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