The square brass plate of side x cm is 1 mm thick and weighs 5.44 kg. If 1 cm³ of brass weighs 8.5 g, find the value of x.
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Question

The square brass plate of side x cm is 1 mm thick and weighs 5.44 kg. If 1 cm3 of brass weighs 8.5 g, find the value of x.

KnowledgeBoat · Accepted Answer

Given,

Side of square = x cm.

Thickness of brass = 1 mm = 0.1 cm

Total weight = 5.44 kg = 5440 g

1 cm³ of brass weighs 8.5 g

Density = 8.5 g/cm³

Calculating the volume of the brass,

Volume of the brass = $\dfrac{\text{Total weight of brass}}{\text{Density of the brass}}$

= $\dfrac{5440}{8.5}$

= 640 cm³.

Calculating the area of the plate,

Area of the plate = length × breadth

= x × x = x²

We know that,

Volume = Area of the plate × Thickness of the brass.

⇒ 640 = x² × 0.1

⇒ x² = $\dfrac{640}{0.1}$

⇒ x² = 6400

⇒ x = $\sqrt{6400}$

⇒ x = 80 cm.

Hence, x = 80 cm.

Mathematics