Question

If each edge of a cube is doubled.
(a) how many times will its surface area increase?
(b) how many times will its volume increase?

Answer 1

Solution :-

Let us Assume That, Each edge of cube is a cm.

Given That, Each edge is doubled .

So, we can say That,

→ New Side of cube = 2 * a = 2a.

So,

→ initial Surface Area of cube = 6(side)² = 6a²

→ New Surface Area of cube = 6*(2a)² = 6*4a² = 24a²

Hence,

→ Number of Times Surface Area increased = (24a²)/(6a²) = 4 Times (Ans).

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Similarly, Now,

→ initial Volume of cube = (side)³ = a³.

→ New Volume of cube = (2a)³ = 8a³.

Hence,

→ Number of Times Volume increased = (8a³)/(a³) = 8 Times (Ans).

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Answer 2

Solution-

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Let the length of the edge of the cube be 'x' cm

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(i) Total surface area = 6x2 cm²

➠ Increased length of the edge = 2x

➠ Total surface area = 6(2x)² cm²= 24x2 cm²

➠If the edge of the cube is doubled surface area of the cube increases by 4 times.

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(ii) Volume of the cube = x³cm³

➠ Increased length of the edge = 2x

➠ Volume of the cube formed = (2x)³ cm³ = 8x cm³

➠ If the edge of the cube is doubled volume of the cube is increases by 8 times

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