Question

A cylindrical piece of metal is 4.5 dm in height with radius of 5.50 x 10^-5 km.

a) Calculate the volume in milliliters to the correct significant figures given V=πr^2h for a cylinder.
b) Calculate the volume in mm^3
c) Calculate the density in units g/L to the correct number of significant figures given the metal has a mass of 6.54 x 10^5 grams

Answer 1

a)
`V=4.3x10^3mL`

b)
`V=4.3x10^6mm^3`

c)
`\rho=1.5x10^5g/L`

Step-by-step explanation:

Hello,

a) In this case, the given height in cm is:

`h=4.5dm*(1m)/(10dm)* (100cm)/(1m)=45cm`

And the radius in cm is:

`r=5.50x10^(-5)km*(1000m)/(1km)*(100cm)/(1m)=5.5cm`

Thus, the volume in cubic centimeters which is also equal in mL (1cm³=mL) is:

`V=\pi (5.5cm)^2*45cm\\\\V=4.3x10^3cm^3=4.3x10^3mL`

b) In this case, the given height in mm is:

`h=4.5dm*(1m)/(10dm)* (1000mm)/(1m)=450mm`

And the radius in mm is:

`r=5.50x10^(-5)km*(1000m)/(1km)*(1000mm)/(1m)=55mm`

Thus, the volume in cubic millimeters is:

`V=\pi (55mm)^2*450mm\\\\V=4.3x10^6mm^3`

c) Finally, since 1000 mL equal 1 L, the required density in g/L turns out:

`\rho=(m)/(V)=(6.54x10^5g)/(4.3x10^3mL)*(1000mL)/(1L)\\ \\\rho=1.5x10^5g/L`

Best regards.