A plate on square base made of brass is of length x cm and width 1 mm. The plate weights 4725 gm. If 1 cubic cm cm of brass weight 8.4 grams, then the value of x is : 

Given:

A plate on square base made of brass is of length x cm and width 1 mm. The plate weights 4725 gm. If 1 cubic cm of brass weighs 8.4 grams.

Concept:

Volume of the plate = Length × Width × Height

Weight of the plate = Volume × Density

Calculation:

We have,

⇒ Weight of the plate = 4725 gm

⇒ Density of brass = 8.4 gm/cm³

Let the height of the plate be h cm (which is 0.1 cm, since 1 mm = 0.1 cm)

⇒ Volume of the plate = x cm × x cm × 0.1 cm

⇒ Volume of the plate = 0.1x² cm³

⇒ Weight of the plate = Volume × Density

⇒ 4725 gm = 0.1x² cm³ × 8.4 gm/cm³

⇒ 4725 = 0.84x²

⇒ x² = 4725 / 0.84

⇒ x² = 5625

⇒ x = √5625

⇒ x = 75 cm

∴ The value of x is 75 cm.