Question
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm, and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, Find the volume of the wood and that of the graphite?
Hint:
The diameter of the pencil consists of both wood and graphite. So, if we subtract graphite from pencil then we will get the wood.
The correct answer is: The volume of wood and graphite are 5280 and 110 cubic mm. respectively.
Explanations:
Step 1 of 3:
The diameter of pencil and graphite are given by 7 mm and 1 mm, respectively. The length of the pencil is 14 cm, i.e., 140 mm (since 1 cm = 10 mm).
The radius of pencil and graphite are given by 3.5(= 
) mm and 0.5(=
) mm, respectively.
Step 2 of 3:
The volume of graphite is 
cubic mm.
The volume of pencil is 
cubic mm.
Step 3 of 3:
If we subtract the volume of graphite from the whole volume of pencil, we would be left with only volume of wood.
Hence, the volume of the wood is 
cubic mm.
Final Answer:
The volume of wood and graphite are 5280 and 110 cubic mm. respectively.
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For the solution of the system of equations above, what is the value of ?
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The equations can be solved in many other ways like substitution
method which is: to eliminate one variable in any one of the
equations with the help of other equation. As we need to find the
value of x, we try to find the value of y in terms of x from one
equation. Then put that value of y in the other equation to get a linear equation in one variable , which is x.
