Question

The length, breadth and height of a room is 16 feet , 12 feet and 10 feet
respectively. How many boxes measure 6 feet long 4 feet wide and 2 feet
high can be arranged in the room? Plz help me with my question.​

Answer 1

GIVEN:

• Length, Breadth and height of room is 16 feet, 12 feet and 10 feet respectively.
• Length, Breadth and height of box is 6 feet, 4 feet and 2 feet respectively.

TO FIND:

• How many boxes can be arranged in a room ?

SOLUTION:

First, we need to find the volume of room

• LENGTH = 16 feet
• BREADTH = 12 feet
• HEIGHT = 10 feet

To find the volume of room, we use the formula:-

$\large{\boxed{\bf{\star \: VOLUME = L \times B \times H \: \star}}}$

According to question:-

➠ VOLUME = 16 $\times$ 12 $\times$ 10

✰ VOLUME = 1920 feet³ ✰

Now, we have to find the volume of box.

• LENGTH = 6 feet
• BREADTH = 4 feet
• HEIGHT = 2 feet

According to question:-

On putting the given values in the above mentioned formula, we get

➠ VOLUME = 6 $\times$ 4 $\times$ 2

⠀✰ VOLUME = 48 feet³ ✰

Number of boxes arranged in room are:-

➨ $\bf{\dfrac{Volume \: of \: room}{Volume \: of \: Box}}$

➨ $\bf{\cancel\dfrac{1920}{48}}$

★ Number of boxes = 40 ★

❝ Hence, the number of boxes arranged in room are 40 ❞

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Answer 2

QUESTION:-

✯ᴛʜᴇ ʟᴇɴɢᴛʜ, ʙʀᴇᴀᴅᴛʜ ᴀɴᴅ ʜᴇɪɢʜᴛ ᴏғ ᴀ ʀᴏᴏᴍ ɪs 16 ғᴇᴇᴛ , 12 ғᴇᴇᴛ ᴀɴᴅ 10 ғᴇᴇᴛ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ. ʜᴏᴡ ᴍᴀɴʏ ʙᴏxᴇs ᴍᴇᴀsᴜʀᴇ 6 ғᴇᴇᴛ ʟᴏɴɢ 4 ғᴇᴇᴛ ᴡɪᴅᴇ ᴀɴᴅ 2 ғᴇᴇᴛ ʜɪɢʜ ᴄᴀɴ ʙᴇ ᴀʀʀᴀɴɢᴇᴅ ɪɴ ᴛʜᴇ ʀᴏᴏᴍ? ᴘʟᴢ ʜᴇʟᴘ ᴍᴇ ᴡɪᴛʜ ᴍʏ ϙᴜᴇsᴛɪᴏɴ.

ANSWER✔

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

$\sf\large\therefore FOR\: ROOM,$

$\sf\dashrightarrow L=16feet$

$\sf\dashrightarrow B=12feet$

$\sf\dashrightarrow H=10feet$

$\sf\large\therefore FOR\:BOX$

$\sf\dashrightarrow L=6feet$

$\sf\dashrightarrow B=4feet$

$\sf\dashrightarrow H=2feet$

$\Large\underline\bold{TO\:FIND}$

$\sf\therefore THE\:NUMBER\:OF\:BOX\:ARRANGED\:IN\:A\:ROOM$

$\sf\large\therefore taking\:two\:cases$

$\sf\therefore in\:case\:1st\:we\:will\:find\:volume\:of\:room\:and\:box$

$\sf\therefore in\:2nd\:case\:finding\:no\:of\:box\:arranged\:in\:a\:room$

$\Large\underline\bold{SOLUTION,}$

$\Large\underline\bold{According\:to\:question}$

$\huge {\fbox {CASE:-1}}$

$\sf\large\therefore finding\:the\:volume\:of\:room(cuboid),$

$\sf\large\therefore FOR\: ROOM,$

$\sf\dashrightarrow L=16feet$

$\sf\dashrightarrow B=12feet$

$\sf\dashrightarrow H=10feet$

$\Large\underline\bold{by\:using\:formula,}$

$\large\bold\therefore VOLUME\:OF\:CUBOID = L \times B \times H$

$\sf\implies 16 \times 12 \times 10$

$\sf\implies 16 \times 120$

$\sf\implies 1920feet^3$

$\large{\boxed{\sf{=1920feet^3}}}$

NOW,

$\sf\large\therefore finding\:the\:volume\:of\:box(cuboid),$

$\sf\large\therefore FOR\:BOX$

$\sf\dashrightarrow L=6feet$

$\sf\dashrightarrow B=4feet$

$\sf\dashrightarrow H=2feet$

$\large\bold\therefore VOLUME\:OF\:CUBOID = L \times B \times H$

$\sf\implies 6 \times 4 \times 2$

$\sf\implies 6 \times 8$

$\sf\implies 48feet^3$

$\large{\boxed{\sf{=48feet^3}}}$

$\huge {\fbox {CASE:-2}}$

$\sf\large\therefore finding\:number\:of\:boxes\:in\:a\:room,$

ACCORDING TO THE QUESTION,

to find the no. of foxes in a room we use,

formula used,

$\sf\implies \dfrac{Volume \: of \: room}{Volume \: of \: Box}$

$\sf\large\implies \dfrac{\cancel {1920}}{ \cancel {48}}$

$\large {\fbox {=40 }}$

$\Large\underline\bold{the\:number\:of\:boxes\:can\:be\:arranged\:is\:48}$

$\sf{\boxed{\sf{the\:number\:of\:boxes\:arranged\:are\:40}}}$

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