A lead pencil is in the shape of right circular cylinder. The pencil is $28 c m$ long and its radius is $3 m m$ . If the lead is of radius $1 m m$ , then find the volume of the wood used in the pencil.

7.04 {c m}^{3}

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7.14 {c m}^{3}

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8.04 {c m}^{3}

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None of these

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Solution

The correct option is A $7.04 {c m}^{3}$
We have,
$h = 28 c m$
$R = 3 m m = 0.3 c m$
$r = 1 m m = 0.1 c m$

We know that the volume of the hollow cylinder
$= π (R^{2} - r^{2}) h$

So,
$= \frac{22}{7} \times ((0.3)^{2} - (0.1)^{2}) \times 28$

$= 22 \times (0.09 - 0.01) \times 4$

$= 88 \times 0.08$

$= 7.04 c m^{3}$

Hence, this is the answer.

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A lead pencil is in the shape of right circular cylinder. The pencil is 28cm long and its radius is 3mm. If the lead is of radius 1mm, then find the volume of the wood used in the pencil.

The correct option is A 7.04cm3We have,h=28 cmR=3 mm=0.3 cmr=1 mm=0.1 cmWe know that the volume of the hollow cylinder=π(R2−r2)hSo,=227×((0.3)2−(0.1)2)×28=22×(0.09−0.01)×4=88×0.08=7.04 cm3Hence, this is the answer.

A lead pencil is in the shape of right circular cylinder. The pencil is $28 c m$ long and its radius is $3 m m$ . If the lead is of radius $1 m m$ , then find the volume of the wood used in the pencil.