Question

A tin of which is 12 cm long 9 cm wide and 4cm deep hold 120g of tea If 1kg of the same tea is packed into a tin which has a 12-cm square base .how tall will the tin have to be?

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Answer 1

Answer:

A tin which is 12 cm long, 9 cm wide and 4 cm deep holds 120 g of tea. If 1 kg of the same tea is packed into a tin which has a 12 cm square base, how tall will the tin have to be ? BASE AREA OF NEW TIN =A=12*12=144 SQ.CM.

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow length(L)=12cm$

$\sf\dashrightarrow breadth(B)=9cm$

$\sf\dashrightarrow height(H)= 4cm$

$\sf\dashrightarrow tin_1\:can\:hold\:120gm\:of\:tea.$

$\sf\dashrightarrow tin_2\: base= 12cm^2$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow HOW\:TALL\:WILL\:THE\:TIN\:HAVE\:TO\:BE?$

✯FORMULA IN USE,

$\large{\boxed{\bf{ \star\:\: VOLUME\:OF\:TIN(CUBOID)= L\times B \times H\:\: \star}}}$

NOTE:- 1 KG = 1000 gm

$\sf\therefore volume \:of\:tin_1=L\times B \times H$

$\sf\implies 12\times 9 \times 4$

$\sf\implies 432 cm^3$

$\rm{\boxed{\bf{ \star\:\:volume\:of\:tin_1= 432cm^3 \:\: \star}}}$

$\sf\therefore tin_1 \:of\:volume\:432cm^3\:holds\:120gm\:of\:tea$

$\large\underline\bold{\therefore \: ACCORDING\: TO\: THE\: QUESTION,}$

$\sf\dashrightarrow \dfrac{120}{432}= \dfrac{1000}{x}$

$\sf\dashrightarrow x= \dfrac{1000 \times 432}{120}$

$\sf\dashrightarrow x= \cancel \dfrac{1000 \times 432}{120}$

$\sf\dashrightarrow x=3600cm^3$

$\rm{\boxed{\bf{ \star\:\: VOLUME\:OF\:TIN_2\:IS\:3600cm^3\:\: \star}}}$

NOW,

$\sf\therefore VOLUME\:OF\:TIN_2=3600cm^3$

$\sf\dashrightarrow L\times B \times H=3600$

$\sf\therefore\green{FOR, \:TIN_2}$

$\sf\therefore LENGTH(L)=12cm$

$\sf\therefore BASE(B)=12cm$

$\sf\therefore HEIGHT(H)=?$

$\sf\dashrightarrow 12 \times 12 \times H=3600$

$\sf\dashrightarrow 144 \times H=3600$

$\sf\dashrightarrow H= \dfrac{3600}{144}$

$\sf\dashrightarrow H= \cancel \dfrac{3600}{144}$

$\sf\dashrightarrow H= 25cm$

$\large{\boxed{\bf{ \star\:\: height\:of\:tin_2\:is\:25cm \:\: \star}}}$

$\large\underline\bold{\:THE\:TIN_2\:IS\:25cm\:TALL.}$

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