Question

A pencil is of length 8 cm and diameter 4.2 mm. Find the number of revolutions it has to make to
cover an area of 264 cm.​

Answer 1

Answer:

264%4.2=62.8

which is 62 revolutions +8 percentage bof the revolution

Answer 2

$\large\underline\blue{\bold{Given \:  Question :-  }}$

A pencil is of length 8 cm and diameter 4.2 mm. Find the number of revolutions it has to make to cover an area of 264 cm^2.

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$\huge \orange{AηsωeR} ✍$

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$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{length \: of \: pencil \: = \: 8 \: cm} \\ &\sf{diameter \: of \: pencil \: = 4.2 \: mm} \\ &\sf{area \: to \: be \: covered \: = 264 \: {cm}^{2} }\end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf To \: Find :- \begin{cases} &\sf{number \: of \: revolutions} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

${{ \boxed{{\bold\green{Curved \: Surface \: Area_{(Cylinder)}\: = \:2\pi rh}}}}}$

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$\large\underline\purple{\bold{Solution :- }}$

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✏Dimensions of pencil :-

✏Length of pencil, h = 8 cm

✏Diameter of pencil = 4.2 mm

✏Radius of pencil, r = 2.1 mm = 0.21 cm.

✏Curved Surface area of pencil =

${{ {{\bold{Curved \: Surface \: Area_{(Cylinder)}\: = \:2 \: \pi \: r \: h}}}}}$

$\sf \: Curved \: Surface \: Area_{(Cylinder)}\: =2 \times \dfrac{22}{7} \times \dfrac{21}{100} \times 8$

$\sf \:  Curved \: Surface \: Area_{(Cylinder)}\: =\dfrac{1056}{100} = 10.56 \: {cm}^{2}$

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✏Let number of revolutions be 'n'.

✏We know, Area covered in 1 revolution by pencil = Curved Surface area of pencil.

✏So area covered in 1 revolution = 10.56 cm^2.

✏So, area covered in n revolutions = 10.56 n cm^2.

✏According to statement,

✏Area covered = 264 cm^2.

$\bf\implies \:10.56 \: n = 264$

$\bf\implies \:n = \dfrac{264}{10.56} = 25$

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✏ More info:

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

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