Question

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.​

Answer 1

Step-by-step explanation:

Letr and hbe the radius and height

Therefore,volume of graphite

=πr²h

=(22÷7(1÷20)².14)cm

=0.11 cm³

Therefore,volume of pensil

= πr²h

=(22÷(7÷20)²14)cm³

=5.39 cm³

Therefore volume of wood=volume of pensil- volume of graphite

=(5.39-0.11)cm³

=5.28 cm

Answer 2

Answer:

★ $\large{\sf{Volume_{(Wood)} = 5280 \: mm^{3}}}$

★ $\large{\sf{Volume_{(Graphite)} = 110 \: mm^{3}}}$

Step-by-step explanation:

$\large{\underline{\sf{Given:-}}}$

$\large{\sf{Diameter_{(Pencil)}\rightarrow{7 \: mm}}}$

$\large{\sf{Diameter_{(Graphite)}\rightarrow{1 \: mm}}}$

$\large{\sf{Length_{(Pencil)}\rightarrow{14 \: cm = 7 \: mm}}}$

$\purple{\star} \: {\large{\underline{\boxed{\sf{Radius = \dfrac{Diameter}{2}}}}}}$

$\large{\leadsto{\sf{Radius_{(Pencil)} = \dfrac{Diameter_{(Pencil)}}{2}}}}$

$\large{\leadsto{\sf{Radius_{(Pencil)} = \dfrac{7}{2}}}}$

$\large{\boxed{\leadsto{\sf{Radius_{(Pencil)} = 3.5 \: mm}}}}$

$\large{\leadsto{\sf{Radius_{(Graphite)} = \dfrac{Diameter_{(Graphite)}}{2}}}}$

$\large{\leadsto{\sf{Radius_{(Graphite)} = \dfrac{1}{2}}}}$

$\large{\boxed{\leadsto{\sf{Radius_{(Graphite)} = 0.5 \: mm}}}}$

$\purple{\star} \: {\large{\underline{\boxed{\sf{Volume_{(Cylinder)} = \pi{r}^{2}h \: \: cubic \: units}}}}}$

$\large{\leadsto{\sf{Volume_{(Pencil)} = \dfrac{22}{\cancel{7}} \times (3.5)^{2} \times {\cancel{140}}}}}$

$\large{\leadsto{\sf{Volume_{(Pencil)} = 22 \times 12.25 \times 20}}}$

$\large{\leadsto{\sf{Volume_{(Pencil)} = 12.25 \times 440}}}$

$\large{\boxed{\leadsto{\sf{Volume_{(Pencil)} = 5390 \: mm^{3}}}}}$

$\large{\leadsto{\sf{Volume_{(Graphite)} = \dfrac{22}{\cancel{7}} \times (0.5)^{2} \times {\cancel{140}}}}}$

$\large{\leadsto{\sf{Volume_{(Graphite)} = 22 \times 0.25 \times 20}}}$

$\large{\leadsto{\sf{Volume_{(Graphite)} = 0.25 \times 440}}}$

$\large{\gray{\boxed{\leadsto{\sf{Volume_{(Graphite)} = 110 \: mm^{3}}}}}}$

$\large{\sf{Volume_{(Wood)} = Volume_{(Pencil)} - Volume_{(Graphite)}}}$

$\large{\leadsto{\sf{Volume_{(Wood)} = (5390 - 110) \: mm^{3}}}}$

$\large{\gray{\boxed{\leadsto{\sf{Volume_{(Wood)} = 5280 \: mm^{3}}}}}}$

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• (1 cm = 10 mm) So, while converting a cm to mm we just need to multiply the cm value with 10.