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Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is
(a) 12 cm
(b) 24 cm
(c) 18 cm
(d) 20 cm

Solution:

Volume of a cube = S³ (where S = side or edge of the cube)

Volume of cube with edge 6 cm = 6 × 6 × 6 = 216 cm³

Volume of cube with edge 8 cm = 8 × 8 × 8 = 512 cm³

Volume of cube with edge 10 cm = 10 × 10 × 10 = 1000 cm³

When these metal cubes are melted the total melted volume is = 216 + 512 + 1000 = 1728 cm³

The new cube which is formed with the melted material will have a volume = 1728 cm³

The edge of the new cube will be:

S³ = 1728

S³ = 12 × 12 × 12

S = 12 cm

Hence the edge of the new cube will be 12 cm.

Answer is choice (a)

✦ Try This: Three cubes of metal whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. The edge of the new cube is (a) 4 cm, (b) 6 cm, (c) 8 cm, (d) 7 cm

Volume of a cube = S³ (where S = side or edge of the cube)

Volume of cube with edge 6 cm = 3 × 3 × 3 = 27 cm³

Volume of cube with edge 8 cm = 4 × 4 × 4 = 64 cm³

Volume of cube with edge 10 cm = 5 × 5 × 5= 125 cm³

When these metal cubes are melted the total melted volume is = 27 + 64 + 125 = 216 cm³

The new cube which is formed with the melted material will have a volume = 216 cm³

The edge of the new cube will be:

S³ = 216

S³ = 6 × 6 × 6

S = 6 cm

Hence the edge of the new cube will be 6 cm.

Answer is choice (b)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 22

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is (a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

Summary:

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is 12 cm

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