Ex.11.4 Q7 Mensuration Solution - NCERT Maths Class 8

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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?

 Video Solution
Ex 11.4 | Question 7

Text Solution

What is Known?

Initial surface area and volume of a cube.

What is unknown?

Increased surface area and volume of a cube.


Whenever sides are doubled in any structure then area becomes four times the original structure and the volume becomes eight times the original structure.


It the initial edge of the cube is \(l \rm\,cm.\)

If each edge of the cube is doubled, then it becomes \(2l\rm\, cm.\)

(i) Initial surface area \(=\) \(6{l^2}\)

New surface area

\[\, = 6{(2l)^2} = 6 \times 4{l^2} = 24{l^2}\]

Ratio \(=\) \(6{l^2}:24{l^2}=1:4\)

(ii) Initial volume of the cube \(= \,{l^3}\)

New volume\(\, = {(2l)^3} = 8 \times {l^3}\)

Ratio \(=\) \({l^3}\): \(8{l^3}\)\(= 1 :8\)

Thus, the surface area will be increased by four times and volume of the cube will be increased by eight times.

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