Question

13. Three cubes having edges 18 cm, 24 cm and 30 cm respectively are melted and made into a new
cube. Find the edge of the new cube so formed.​

Answer 1

Answer:

36cm

Step-by-step explanation:

Question says that, Three cubes of edges 18cm, 24cm, and 30cm are melted to form a new single cube. find the edge of the new cube.

Step 1 : Find the volume of the individual cube :

Volume of a cube is given by : (each edge)³

• each edge of the first cube is 18cm.

So,

→ (18)³

→ 5,832cm³

Volume of the second cube :

→ (24)³

→ 13,824cm³

Volume of the third cube :

→ (30)³

→ 27,000cm³

Now, they are melted and a single cube is formed

The volume of the new cube will be the sum of the three cubes :

→ 5,832 + 13,824 + 27,000

→ 46,656cm³

∴ The volume of the new cube is 46,656cm³

Step 2 : Find the each edge of new cube :

We know that,

Volume of the new cube = (each edge)³

But, the volume of the new cube is 46,656cm³

So,

→ 46,656 = (each edge)³

→ ³√46,656 = each edge

→ 36cm = each edge.

∴ Each edge of the new cube is 36cm

Answer 2

$\textsf{The edge of the new cube = 36 cm}$

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$\large\underline{\red{\sf \orange{\bigstar} Given:-}}$

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• $\textsf{Firstly take the three edges as A, B, C}$

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• $\textsf{Edge of cube A = 18 cm}$

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• $\textsf{Edge of cube B = 24 cm}$

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• $\textsf{Edge of cube C = 30 cm}$

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$\large\underline{\pink{\sf \red{\bigstar} To Find:-}}$

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• $\textsf{The edge of new cube ? }$

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$\large\underline{\blue{\sf \orange{\bigstar} Solution:-}}$

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• $\textsf{→"Volume of cube = a³"}$

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• $\textsf{and, a = edge}$

Now,

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$\blue{\sf{\star\;Volume \;of\; cube\; A!}}$

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• $\textsf{⇒V1= (18)³}$

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• $\textsf{⇒5832cm³}$

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$\red{\sf{\star\;Volume \;of \;cube\; B! }}$

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• $\textsf{⇒V₂ = (24)³}$

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• $\textsf{⇒13824cm³}$

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$\green{\sf{\star\;Volume \;of \;cube \;C!}}$

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• $\textsf{⇒V₃ = (30)³}$

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• $\textsf{⇒27000cm³}$

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$\pink{\sf{\star\;Total \;volume\; of \;cube \;A\;, B, \;C}}$

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• $\textsf{⇒(5832 + 13824 + 27000)cm³}$

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• $\textsf{⇒46656cm³}$

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• $\textsf{Let a be the edge of new cube}$

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• $\textsf{∴Volume = a³ = 46656}$

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• $\textsf{a = ∛46656}$

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• $\textsf{⇒∛6 × 6 × 6 × 6 × 6 × 6}$

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• $\textsf{⇒6 × 6}$

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• $\textsf{⇒36cm³}$

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• $\textsf{Therefore, the volume of  edge of the new cube is "36cm³}$

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$\textsf{Note :-}$

• $\textsf{For viewing answer completely slide the answer from right to left!}$