Question

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

Answer 1

The necessary amount of wood is 1212.75 cm³.

Given data :

Diameter of the pencil = 10.5 mm

Length of the pencil = 14.4 cm = 144 mm

Lead's diameter = 1.75 mm

Now,

Radius of the pencil = 10.5/2 = 5.25 mm

Volume of a pencil = π × 5.25 × 5.25 × 144 = 12474 mm³

Radius of lead = 1.75/2 = 0.875 mm

Volume of lead = π × 0.875 × 0.875 ×144 = 346.5 mm³

Wood's volume in one pencil = (12474-346.5) = 12127.5 mm³

Wood's volume in 100 pencils = 12127.5 × 100 = 1212750 mm³ = 1212.75 cm³ (answer)

Answer 2

$\huge\mathfrak\red{Answer:}$

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 =

$= 100 \times 0.3465$

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