The density of titanium is 4.51 gcm3. What is the volume (in
cub...

Question

The density of titanium is 4.51 g>cm3. What is the volume (in
cubic inches) of 3.5 lb of titanium?

Accepted Answer

Welcome back everyone. We need to calculate the volume and cubic interest of £1.6 of gold. Given that its density is 19.3 g per cubic centimeter. So what we're going to recognize is that we're going to be going through a conversion or a series of unit conversions rather. So beginning with the unit that were given for the massive golden pounds, we're going to want to go from pounds to kilograms from kilograms to grams from grams to cubic centimeters and then finally from cubic centimeters to our final unit for volume in inches, cute as the prompt states. And so let's begin with our massive gold as £1. of gold. We're going to multiply by our first conversion factor to convert from pounds in the denominator, two kg in the numerator. And we want to recall our conversion factor from our textbooks where £2.2 is equivalent to one kg. This allows us to cancel our units of pounds and now we're going to focus on converting from kilograms to grams in the numerator, recall that our prefix kilo tells us that we have 10 to the third power of our base unit gram. So canceling out kilograms were now left with gramps and now we can focus on incorporating the density given for gold in the prompt as a conversion factor where we will interpret that we have 19.3 g per cubic centimeter as our density. And so this allows us to not cancel out grams and now focus on going from cubic centimeters to our final conversion as cubic inches. But we should recall the conversion factor from our textbooks where 2.54 cm is equivalent to one inch. Now recognize that we need cubic, sorry, cubic inches as the prompt states. And so we're going to have to take this entire conversion factor and multiply it by a factor of three. And so now canceling out our units of cubic centimeters. We're left with cubic inches because we have this entire conversion factor again raised to the root of three. And this will yield a result equal to a value of about 2.29 in which we can round two. Exactly two. Sig figs as our minimum number of sig figs being 2. cubic inches. And what's highlighted in yellow here is our final answer as our volume of gold. So I hope that this made sense. And let us know if you have any questions.

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