Question

1 m^3 = 1000dm^3.true or false

Answer 1

Answer:

True

Explanation:

1 m = 10¯¹ dm

∴ 1 m = 1 / 10 dm

∴ 1 m = 0.1 dm ..... ( 1 )

Now,

1 m³ = 1 m × 1 m × 1 m = 1 m

Also,

1 dm³ = 1 dm × 1 dm × 1 dm

∴ 1 dm³ = 0.1 m × 0.1 m × 0.1 m .... [ From ( 1 ) ]

∴ 1 dm³ = 0.001 m³ ......( 2 )

Now, by multiplying both sides by 1000 in equation ( 2 ), we get,

1000 dm³ = 1000 × 0.001 m³

∴ 1000 dm³ = 1 m³

i. e. 1 m³ = 1000 dm³

Hence, the given statement is true.

Additional Information :

1] 1 m = 0.1 dm

Here, m → metre

dm → decimetre

2] 1 m = 0.01 cm

Here, m → metre

cm → centimetre