Question

Convert 1 square metre in square centimetres

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

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

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

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

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

Hence 1 square metre = 10,000 square centimetres.

Hence option (a) is correct.

Note:  

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

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.