Question

Three cubes with length of edges 3 cm, 4 cm and 5 cm are melted and recast into a single cube. Find
the TSA of new cube formed.​

Answer 1

$\large{\bf{ \underline{ \underline{ \purple{Answer :}}}}}$

$\bullet$ TSA (Total surface area) of new cube formed is 216 cm².

Given :

• Three cubes with length of edges 3 cm, 4 cm & 5 cm are melted and recast into a single cube.

To Find :

• TSA (Total surface area) of new cube formed.

Calculation :

Here we are provided with the length of edges 3 cm, 4 cm and 5 cm. And we need to calculate the total surface area of new cube formed. Firstly, we need to calculate the volume of the three cubes, by performing addition :-

• $\underline{ \bf{ \pmb{ \blue{Volume_{(cube)} \: = Sum \: of \: all \: cubes }}}}$

$\dag$ Putting the values,

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$: \: \Longrightarrow \sf Volume_{(cube)} = 3^3 \: cm + 4^3 \: cm + 5^3 \: cm$

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$: \: \Longrightarrow \sf Volume_{(cube)} = (3 \times 3 \times 3) + (4 \times 4 \times 4) + (5 \times 5 \times 5) \: cm$

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$: \: \Longrightarrow \sf Volume_{(cube)} = 27 \: cm + 64 \: cm + 125 \: cm$

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$: \: \Longrightarrow { \boxed{\sf Volume_{(cube)} = 216 \: cm^3}} \: \red{ \bigstar}$

Therefore, volume of the cube is 216 cm³.

Now, we will calculate the side of one cube,

As we know that,

• $\boxed{ \rm{ \gray{Side_{(cube)} \: = \: a^3}}}$

~ Putting the values,

$: \: \Longrightarrow \sf \: a^3 = 216 \: cm^3$

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$: \: \Longrightarrow{ \boxed{\sf \: a^3 = 6 cm}} \: \pink{ \bigstar}$

Hence, side of one cube is 6 cm.

$\dag$ According to the Question,

~ Calculating the TSA (Total surface area) of new cube,

As we know that,

• $\boxed{ \rm{ \gray{TSA_{(cube)} \: = \: 6a^2}}}$

Putting the values,

$: \: \Longrightarrow \sf TSA_{(cube)} \: = 6 a^2$

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$: \: \Longrightarrow \sf TSA_{(cube)} \: = 6 \times 6^2$

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$: \: \Longrightarrow \sf TSA_{(cube)} \: = 6 \times 6 \times 6 cm^2$

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$: \: \Longrightarrow { \boxed{ \sf TSA_{(cube)} = 216 \: cm^2 }} \: \green{ \bigstar}$

Therefore, TSA (Total surface area) of new cube is 216 cm².

Answer 2

Given :-

• Three cubes with length of edges 3 cm, 4 cm and 5 cm are melted and recast into a single cube.

To Find :-

• T.S.A of New cube formed

Solution :-

❏ In this question, firstly we will find the volume of the Three cubes separately, then we will find total volume of the cube after that we will find the side of the cube then we can easily find the Total Surface Area of cube by applying [ T.S.A of Cube = 6 × (side)² ]

Let's do it !!

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➞ Volume of 1st Cube = (side)³

➞ Volume of 1st Cube = (3)³

➞ Volume of 1st Cube = 3 × 3 × 3

➞ Volume of 1st Cube = 9 × 3

➞ Volume of 1st Cube = 27cm³

________________

➞ Volume of 2nd Cube = (side)³

➞ Volume of 2nd Cube = (4)³

➞ Volume of 2nd Cube = 4 × 4 × 4

➞ Volume of 2nd Cube = 16 × 4

➞ Volume of 2nd Cube = 64cm³

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➞ Volume of 3nd Cube = (side)³

➞ Volume of 3nd Cube = (5)³

➞ Volume of 3nd Cube = 5 × 5 × 5

➞ Volume of 3nd Cube = 25 × 5

➞ Volume of 3nd Cube = 125cm³

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Total Volume of new Cube :

⟾ Total Volume = 1st + 2nd + 3rd

⟾ Total Volume = 27 + 64 + 125

⟾ Total Volume = 91 + 125

⟾ Total Volume = 216cm³

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Side of New Cube :

⠀⠀⠀⠀⠀⠀➟ Volume of Cube = (side)³

⠀⠀⠀⠀⠀⠀➟ 216 = (side)³

⠀⠀⠀⠀⠀⠀➟ ³√216 = side

⠀⠀⠀⠀⠀⠀➟ 6cm = side

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Total Surface Area of Cube :

⤳ T.S.A of Cube = 6 × (side)²

⤳ T.S.A of Cube = 6 × (6)²

⤳ T.S.A of Cube = 6 × 6 × 6

⤳ T.S.A of Cube = 36 × 6

⤳ T.S.A of Cube = 216cm²

Thus, Total Surface Area of New Cube is 216cm²

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