# Ex.11.4 Q7 Mensuration Solution - NCERT Maths Class 8

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## Question

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
Mensuration
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.

Reasoning:

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

Steps:

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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