Question

Convert 1 square metre in square centimetres

a) $1{\text{m}}^2=10000\text{ c}{\text{m}}^2$

b) $1{\text{m}}^2=1000\text{ c}{\text{m}}^2$

c) $1{\text{m}}^2=100\text{ c}{\text{m}}^2$

d) $1{\text{m}}^2=10\text{ c}{\text{m}}^2$

Answer 1

Hint: Use 1m = 100cm. Substitute this value in place for every m in the LHS. Hence find the value of the quantity. This will give the result of the above conversion.

Complete step-by-step answer:

We know that 1m = 100cm.

Now $1{\text{m}}^2=\left(1\text{ m}\right)\left(1\text{ m}\right)=\left(100\text{ cm}\right)\left(1\text{00 cm}\right)=10000\text{ c}{\text{m}}^2$

Hence 1 square metre = 10,000 square centimetres.

Hence option (a) is correct.

Note:  

The area of a square with side 1m $={\left(1\text{ m}\right)}^2=1{\text{m}}^2$

Also the area of a square with side 100cm $={\left(100\text{ cm}\right)}^2=10000\text{ c}{\text{m}}^2$

Since 1m = 100cm, the squares have equal area.

Hence, we have

1 square metre = 10,000 square centimetres.

Hence option (a) is correct.