Question

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A pencil of diameter 10.5 mm and length 14.4 cm has a lead of diameter 1.75mm. Find the volume of the word and of the lead used in making 100 pencils.


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Answer 1

$\huge\tt\purple{Answer:}$

Diameter = 10.5mm

Length= 14.4

Lead diameter = 1.75 mm

Diameter of pencil = 10.5mm= 10.5/10 cm

Radius of pencil (r1) =10.5/20=0.525 cm

Radius of lead (r2) = 1.75/20cm=0.0875 cm

Height of pencil (h) =14.4 cm.

Volume of wood in pencil=

$= \pi(r1^{2} - r2^{2} )h$

$= \frac{22}{7} ((0.525)^{2} - ({0.0875}^{2} )) \\ 14.4$

= 22/7(0.275625-0.00765625)14.4

$= \frac{22}{7} \times 0.27 \times 14.4$

$= 12 .21cm ^{3}$

Volume of wood in 100 pencils=

= 100 x 12.21 cm^3

=

$1221 {cm}^{3}$

Volume of lead =

$= \pi \: r2 ^{2} h$

$= \frac{22}{7} \times {0.0875}^{2} \times 14.4$

$= 0.3465 \: {cm}^{2}$

Volume of lead in 100 pencils =

$= 100 \times 0.3465$

$= 34.65 \: {cm}^{2}$

Answer 2

${\huge{\star{\red{\bold{\boxed{\boxed{Answer}}}}}}}{\huge{\star}}$

${\pink{\huge{225\: steps}}}$

⭐${\blue{\huge{Explanation}}}$⭐

Volume of pencil = πr²h

= 22/7 × 10.5 × 10.5 × 1440

Volume of lead = πr²h

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