Given $rho_"gold"=19.3gcm^-3$ , will a thief set off a mass-activated alarm if he steals a gold cylinder which is $22cm$ long, and which has a diameter of $7.6cm$ , and replaces the gold bar with a bag of sand whose mass is $3*kg$ ?

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Given $rho_"gold"=19.3gcm^-3$ , will a thief set off a mass-activated alarm if he steals a gold cylinder which is $22cm$ long, and which has a diameter of $7.6cm$ , and replaces the gold bar with a bag of sand whose mass is $3*kg$ ?

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Answer 1 · 2016-09-05T06:47:44

Yes, the tea leaf sets off the alarm.

Explanation:

The question is asking you to use density, $rho$ , which is $"mass"/"volume"$ , and usually has units of $g*cm^-3$ or $g*mL^-1$ in order to determine the mass of each substance.

Since $"density, "rho$ $=$ $"Mass"/"Volume"$ , $"mass"="volume"xxrho$ . The volume of a cylinder is $pi*r^2*l$ , where $"l"$ is cylinder length.

I need to find (i) the volume of the cylinder $=$ $pixx"radius"^2xx"length"$ , and (ii) the mass of the substance it contains, $=$ $rhoxx"volume"$ .

$"Mass of gold"$ $=$ $19.3*g*cancel(cm^-3)xxpixx3.8^2*cancel(cm^2)xx22*cancel(cm)$

$=$ $19252*g$ .

$"Mass of sand"$ $=$ $3.0*g*cancel(cm^-3)xxpixx3.8^2*cancel(cm^2)xx22*cancel(cm)$

$=$ $2993*g$ .

Given that gold is currently selling for $$1326*USD*"oz"^-1$ ( $1*"oz"=28.5*g$ ), how much do you think that gold bar is worth?

Just to add that a $"bag of sand"$ is cockney rhyming slang for a $£1000-00$ , and this amused me....

Answer 2 · 2016-09-05T07:57:07

Refer to the explanation.

Explanation:

First determine the volume of the cylinders. Then use the densities of the sand and gold to calculate their masses.

$V_"cylinder"=pi*r^2*h$ , where $pi$ is pi (I'm going to use the $pi$ button on my calculator), $r$ is the radius, and $h$ is the height.

Since no units for the radius and height (length) are given, but your densities are given in $"g/cm"^3"$ , I'm going to use centimeters.

$V_"cylinder"=pi*(3.8 "cm")^2*22 "cm"="998 cm"^3"$

Now we'll use the volume of the cylinders and the densities of sand and gold to determine their masses.

$"density"=("mass")/("volume")"$

We can rearrange the equation to determine mass.

$"mass"="density"xx"volume"$

Determine the mass of sand.

$"mass"_"sand"=3.00 "g"/cancel"cm"^3xx998 cancel"cm"^3=3.0xx10^3 "g"$ (rounded to two significant figures)

Determine the mass of gold.

$"mass"_"gold"=19.3 "g"/cancel"cm"^3xx998 cancel"cm"^3=19000 "g"$ (rounded to two significant figures)

As you can see, the sand's mass is much lower than that of the gold, so the alarm would be expected to go off.

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Given $rho_"gold"=19.3gcm^-3$ , will a thief set off a mass-activated alarm if he steals a gold cylinder which is $22cm$ long, and which has a diameter of $7.6cm$ , and replaces the gold bar with a bag of sand whose mass is $3*kg$ ?

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Given rho_"gold"=19.3*g*cm^-3rho_"gold"=19.3*g*cm^-3, will a thief set off a mass-activated alarm if he steals a gold cylinder which is 22*cm22*cm long, and which has a diameter of 7.6*cm7.6*cm, and replaces the gold bar with a bag of sand whose mass is 3*kg3*kg?

2 Answers

Explanation:

Explanation:

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Given $rho_"gold"=19.3gcm^-3$ , will a thief set off a mass-activated alarm if he steals a gold cylinder which is $22cm$ long, and which has a diameter of $7.6cm$ , and replaces the gold bar with a bag of sand whose mass is $3*kg$ ?