Question

${\large{\bf{\red{\underline{\green{\bf{Question :}}}}}}}$
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.


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Answer 1

Given :-

• The diameter of pencil = 7mm
• The diameter of graphite = 1mm
• The height of the pencil = 14cm
• The height of the graphite = 14cm

To Find :-

• The volume of wood having with graphite = ?

Solution :-

To calculate the volume of wood at first we have to find the radius of pencil and graphite. Then calculate the volume of pencil and graphite. After that we have to calculate the volume of wood by subtracting the volume of pencil and the volume of graphite. As given in the question pencil and graphite has same length. Only the difference are their diameter. Here , pencil and and graphite are in cylindrical shape. Because graphite is the filled inside The pencil.

Calculation for pencil :-

Diameter = 7mm. Height = 14cm :-

⟶ Radius = Diameter/2

⟶ Radius = 7/2mm

⟶ Radius = 7/2 × 1/10 = 7/20cm

Volume of pencil :-

⟶ Volume = π × r² × h

⟶ Volume = 22/7 × 7/20 × 7/20 × 14

⟶ Volume = 22/7 × 49/400 × 14

⟶ Volume = 22 × 7 × 14/400

⟶ Volume = 2156/400

⟶ Volume = 5.39cm³

Calculation for graphite :-

Diameter = 1mm. Height = 14cm :-

⟶ Radius = Diameter/2

⟶ Radius = 1/2mm

⟶ Radius = 1/2 × 1/10 = 1/20cm

Volume of graphite :-

⟶ Volume = π × r² × h

⟶ Volume = 22/7 × 1/20 × 1/20 × 14

⟶ Volume = 22 × 2/400

⟶ Volume = 44/400

⟶ Volume = 0.11cm³

Calculation for wood :-

⟶ Volume = Volume_(pencil) - Volume_(graphite)

⟶ Volume = 5.39 - 0.11

⟶ Volume = 5.28cm³

Hence, The volume of wood having graphite = 5.28cm³

Answer 2

Given : 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.

Need to Find : The volume of wood and graphite

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★ Cᴏɴᴄᴇᴘᴛ :

According to the question, here we are provided with pencil and graphite which has a diameter of 7mm and 1mm. Now, as we know that graphite in always placed inside the pencil which helps us to write something. Now, the length of the pencil is 14 cm. First we need to get the volume of pencil using the formula for getting the volume of cylinder as a pencil is cylindrical in shape. The. using the same formula we can get the volume of wood. After which subtracting the volume of graphite from the volume of pencil we can get the volume of wood as well.

★ Sᴏʟᴜᴛɪᴏɴ :

Given Data

Diameter of pencil = 7 mm

As we know that radius is the half of diameter

So, radius (r) = 7/2 mm

Now, on the other hand

Diameter of Graphite = 1 mm

Radius (R) = 1/2 mm

Length of the pencil = 14 cm

[The length of the pencil is in cm. So we need to convert it into mm]

Hence, length = 140 mm

$\star \quad \underline{ \boxed{ \green{\frak{Volume _{(graphite)} = \pi {r}^{2} h}}}} \\ \\ \dashrightarrow \frak{Volume _{(graphite)} = \frac{22}{7} \times {( \frac{1}{2}) }^{2} \times 140} \\ \\ \dashrightarrow \frak{Volume _{(graphite)} = \frac{22}{7} \times \frac{1}{4} \times 140} \\ \\ \qquad \frak{ \red{Volume _{(graphite)} = 110 \: m {m}^{3}}}$

Now, finding the volume of pencil

$\star \quad \underline{ \boxed{ \green{\frak{Volume _{(pencil)} = \pi { \mathcal{R}}^{2} h}}}} \\ \\ \dashrightarrow \frak{Volume _{(pencil)} = \frac{22}{7} \times {( \frac{7}{2}) }^{2} \times 140} \\ \\ \dashrightarrow \frak{Volume _{(pencil)} = \frac{22}{7} \times \frac{49}{4} \times 140} \\ \\ \qquad \frak{ \pink{Volume _{(pencil)} = 5390\: m {m}^{3}}}$

$\frak{Volume _{(pencil)} = \frac{5390}{1000} = 5.39 \: c {m}^{3} }$

Finding Volume of wood

$\frak{Volume _{(wood)} = Volume _{(pencil)} - Volume _{(graphite)}} \\ \\ \frak{Volume _{(wood)} = 5390 \: m {m}^{3} - 110 \: m {m}^{3} } \\ \\ \blue{\frak{Volume _{(wood)} = 5280 \: m {m}^{3}}}$

Now,

$\frak{Volume _{(wood)} = \frac{5280}{1000} = 5.28 \: c {m}^{3} }$

• Required Answer is 5.28 cm³ and 5.39 cm³