Question

A factory manufactures 1500 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Find the cost of
colouring the curved surfaces of the pencils manufactured in one day at Rs 5 per dm²​

Answer 1

${\fcolorbox{blue}{blue}{\huge{Answer}}}$

Given :

ㅤㅤㅤ➪ Total pencils = 1500

ㅤㅤㅤ➪ $\sf{Length_{(pencil)}}$ = 25 cm

ㅤㅤㅤ➪ $\sf{Circumference_{(base)}}$ = 1.5 cm=2πr

ㅤㅤㅤ➪ $\sf{Cost_{(colouring)}}$ per cm² = Rs 5

To Find :

• Cost of colouring the Curved surface of all the pencils produced in the factory in one day

Formula Usable :

• $\sf{C.S.A._{(cylinder)}}$ = 2πrh

•°• Solving the problem :

ㅤㅤ➪ C.S.A of the pencil = 2πr h

ㅤㅤ➪ㅤ "ㅤㅤ"ㅤ"ㅤㅤ"ㅤ= (1.5)×h [given]

ㅤㅤ➪ㅤ "ㅤㅤ"ㅤ"ㅤㅤ" ㅤ = 1.5 × 25

ㅤㅤ➪ㅤ "ㅤㅤ"ㅤ"ㅤㅤ" ㅤ = 37.5 cm²

$\underline{\sf{ \because \:Cost_{(colouring)} \: per\:m^{2} \:=\: Rs\:5 }}$

Now ,

• Cost of colouring of all the pencils produced in a day

• Total length of all pencil ➪

ㅤㅤㅤㅤㅤㅤ= 1500 × 37.5 m

ㅤㅤㅤㅤㅤㅤ= 56250.0 m

ㅤㅤㅤㅤㅤㅤ= 56250 m

•°• Cost of colouring all the pencils produced in one day :

ㅤㅤㅤ➪ 5 × 56250

ㅤㅤㅤ➪ Rs $\boxed{\sf{\red{2,81,250}}}$

_____________________

More to remember :

• C.S.A of cylinder = 2πrh

• T.S.A of cylinder = 2πr(r+h)

ㅤㅤㅤ

ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂

Answer 2

${\fcolorbox{blue}{m}{\huge{Answer}}}$

Given :

ㅤㅤ ㅤ➪ Total pencils = 1500

$\sf{ㅤㅤㅤ➪ Length_{(pencil)}} = 25 \: cm$

$➪ \sf{Circumference_{(base)}}Circumference </p><p>(base)</p><p> </p><p> = 1.5 cm=2πr</p><p>$

$➪ \sf{Cost_{(colouring)}}Cost </p><p>(colouring)</p><p> </p><p> per cm² = Rs 5$

ㅤㅤㅤ

To Find :

Cost of colouring the Curved surface of all the pencils produced in the factory in one day

Formula Usable :

$\sf{C.S.A._{(cylinder)}}C.S.A. </p><p>(cylinder)</p><p> </p><p> = 2πrh$

•°• Solving the problem :

ㅤㅤ➪ C.S.A of the pencil = 2πr h

ㅤㅤ➪ㅤ "ㅤㅤ"ㅤ"ㅤㅤ"ㅤ= (1.5)×h [given]

ㅤㅤ➪ㅤ "ㅤㅤ"ㅤ"ㅤㅤ" ㅤ = 1.5 × 25

ㅤㅤ➪ㅤ "ㅤㅤ"ㅤ"ㅤㅤ" ㅤ = 37.5 cm²

$\underline{\sf{ \because \:Cost_{(colouring)} \: per\:m^{2} \:=\: Rs\:5 }}$

Now ,

Cost of colouring of all the pencils produced in a day

Total length of all pencil ➪

ㅤㅤㅤㅤㅤㅤ= 1500 × 37.5 m

ㅤㅤㅤㅤㅤㅤ= 56250.0 m

ㅤㅤㅤㅤㅤㅤ= 56250 m

•°• Cost of colouring all the pencils produced in one day :

ㅤㅤㅤ➪ 5 × 56250

ㅤㅤ

$\bold {ㅤ➪ Rs} \boxed{\sf{\red{ㅤ➪2,81,250}}} </p><p>$

_____________________

More to remember :

C.S.A of cylinder = 2πrh

T.S.A of cylinder = 2πr(r+h)

ㅤㅤㅤ

ㅤㅤ