Suppose you have a rectangualr wooden block with dimensions 8.0 cm x 8.0 cm x 9.

Question

Suppose you have a rectangualr wooden block with dimensions 8.0 cm x 8.0 cm x 9.0 cm that has a density of 0.85 x 103 kg/m3. The block has a cylindrical hole inside it so that a lead cylinder 5.0 cm in dimater and 7.5 cm high can be fitted completely inside. Please explain and show work.
A) What is the volume of the lead cylinder that fits inside (in m3)?
Here is where I am having trouble:
volume of cylinder= pi*r2*h
V=0.1471*10^-3m^3 ---> I don't understand where these numbers came from??
B) What is the mass of the lead cylinder? (The density of lead = 1.13 x 104).
C) What is the volume of the wood in the wooden block (excluding the volum of the cylindrical hole)?

Explanation / Answer

Here:

pi=3.14; h=7.5cm=0.075m and r=5cm/2=2.5cm=0.025m

Volume of cylinder=pi*r^2*h
a)V=0.075m*3.14*(0.025m^2)=0.147*10^-3m^3
b)mass=density*Volume=1.6632kg
c)volume of wood=0.08*0.08*0.09-0.147*10^-3=0.429*10^-3m^3

volume of cylinder =pi *r^2*h= 589.0486/4=147.262 cm^3
mass of cylinder= density*vol
=1.13*10^4*147.262*10^-6
=1.6640kg

vol of rectangle=l*h*b
=9*8*8=576 cm3
Volume of wood in the wooden block=576-147.262=418.738 cm3

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