Question

two cuboids of dimensions 13cm*6cm*4cm are melted to form a single cube.find the edge of new cube.

Answer 1

• The side of new cube is 2√78 cm.

Step-by-step explanation:

Given:-

• Two cuboids of dimensions 13cm×6cm×4cm.

To Find:-

• Edge of the new cube formed on melting two given Cuboids.

Formula used:-

• Volume of Cuboid = l × b × h

• Volume of Cube = (Side)³

Solution:-

As given,

• l = 13 cm
• b = 6 cm
• h = 4 cm

Putting values in the Formula,

Volume of two Cuboid = 2(l × b × h)

Volume of two Cuboid = 2(13 × 6 × 4)

Volume of Cuboid = 2 × 312

Volume of Cuboid = 624 cm³

These two Cuboids melted to form a cube. So,

Volume of Cube = (Side)³

624 = (Side)³

$Side = \sqrt[3]{624}$

Side = 2√78 cm

Hence, the side of the new cube formed is 2√78 cm.

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Answer 2

Three cuboid of dimension 5cm×6cm×7cm

4cm×7cm×8cm & 2cm×3cm×13cm

are melted & converted into cube.

Cuboid 1=5cm×6cm×7cm …………(1)

Cuboid 2=4cm×7cm×8cm ………….(2)

Cuboid 3=2cm×3cm×13cm ……………(3)

Now volume of cuboid (1+2+3)= volume of cube (2)

Let 'a' be the edge of cube formed then

Volume of cuboid 1=lbh=210cm

Volume of cuboid 2=lbh=224cm

Volume of cuboid 3=lbh=78cm

From equation (4) we get

${a}^{3} = 210 + 224 + 78$

${a}^{3} = 512$

${a}^{3} = ( {8})^{3}$

$(a = 8)$

Hence edge of cube is 8cm.