QUESTION

CSAT

Hard

Maths

Prelims 2016

A piece of tin is in the form of a rectangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is

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Explanation

We are given a rectangular piece of tin with an area of: Area of Tin Piece = Length * Width Area of Tin Piece = 12×8=9612 \times 8 = 96 cm² For a closed cube, the surface area is given by the formula:

Surface Area of Cube = 6×(Side length)26 \times (\text{Side length})^2 Let the side of the cube be x. So, the total surface area of the cube is:

Surface Area of Cube = 6×x26 \times x^2 Since the area of the tin piece is used to cover the surface area of the cube, we equate the two: 6×x2=966 \times x^2 = 96

Solving for x: x2=96/6x^2 = 96 / 6 x2=16x^2 = 16 x=16x = \sqrt{16} x=4x = 4 cm

Thus, the side of the cube is 4 cm.

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