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

## 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?

## 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.