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A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is
(a) 6 cm
(b) 8 cm
(c) 12 cm
(d) 24 cm

Solution:

The amount of material required to build a shape is the volume of the shape which is made from that material. Therefore,

The volume of the Metal Sheet(V) is:

V = length × breadth × thickness

V = 27 × 8 × 1

V = 216 cm³

If a cube is made by melting this metal then the side of the cube will be determined as follows:

Volume (V) of the material melted = 216 cm³

The Volume(Vcube) of the cube made from the material = S³

Where S = side of the cube

Vcube = 216 = S³

S³ = 216

S³ = 6 × 6 × 6

S = 6 cm

Therefore the side of the cube will be 6 cm

The correct choice of answer is (a)

✦ Try This: A metal sheet 27 cm long, 16cm broad and 4cm thick is melted into a cube. The side of the cube (a) 6 cm, (b) 8 cm, (c) 12 cm, (d) 24 cm

The amount of material required to build a shape is the volume of the shape which is made from that material. Therefore,

The volume of the Metal Sheet(V) is:

V = length × breadth × thickness

V = 27 × 16 × 4

V = 1728 cm³

If a cube is made by melting this metal then the side of the cube will be determined as follows:

Volume (V) of the material melted = 216 cm³

The Volume(Vcube) of the cube made from the material = S³

Where S = side of the cube

Vcube = 216 = S³

S³ = 1728

S³ = 12 × 12 × 12

S = 12cm

Therefore the side of the cube will be 12 cm

The correct choice of answer is (c)

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 21

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is (a) 6 cm (b) 8 cm (c) 12 cm (d) 24 cm

Summary:

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is 6 cm

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