the dimensions of your cylinder, which use the least amount of steel. After you have that value, since you have h in terms of r, you can solve for the other value, and thus you will have your h and r, i.e. The ideal gas equation is a mathematical equation that describes the relationship between pressure, volume, number of mole of gas, and the temperature of. Once you have h in terms of r, you can turn the equation A into one of only on variable and then find the value of that variable which minimizes A. But I would suggest you work again on solving for h in the equation: 100=(2/3)(pi)(r3) + (pi)(r2 )(h) We know the formulas for the volume and surface area of a sphere, so we want to find the values of r and h which minimize A, but we see from our relationship of V that there is a restriction between the two which can be seen exactly as you did by solving for h in terms of r. In other words, we want the minimum surface area possible such that we can create a cylinder which holds 100m 3 of whatever we fill it with. We want our volume to be 100m 3 but we want the minimum amount of steel that will create such a cylinder.
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