Question

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If each edge of a cube is doubled,
(i) How many times will its surface area increase?
ii) How many times will its volume increase?
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Answer 1

Answer:

Answer⤵

i)Let the length of the edge of the cube be 'x' cm (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. (ii) Volume of the cube = x3 cm3 Increased length of the edge = 2x Volume of the cube formed = (2x)3 cm3 = 8x3 cm3 If the edge of the cube is doubled volume of the cube is increases by 8 times.

ii)Consider that the side of a cube is S.Volume of a cube will be.Vc=S³ of cubic unitsWhen each side of a cube is doubled,Volume becomes,Vc=(2S)³ of cubic units =8S³Which means that the volume which has increased is 7S³ and it's 7 times the original volume ,

Answer 2

Answer:

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⇒(i) Initial surface area =6×l×l

New surface area =6×(2×l)×(2×l)=4× initial surface area.

So, the new surface area will be increased by 4 times.

⇒(ii) Intial volume =l×l×l

Final volume =(2l)×(2l)×(2l)=8× initial volume.

So, volume of the cube will be increased by 8 times.

❤Adyasha here❤