# How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

**Solution:**

A figure is drawn to visualize the shapes.

From the figure, it can be seen that the shape of the silver coin is cylindrical.

As we know that the silver coins to be melted and recast into a single solid cuboid then the cuboid formed by recasting these coins will be the same in volume as the sum of the volumes of these coins.

Sum of the volumes of the silver coins = Volume of the cuboid

Therefore,

Number of the coins × volume of each coin = Volume of the cuboid

We will find the volume of the solid by using formulae;

Volume of the cuboid = lbh, where l, b, and h are the length, breadth, and height of the cuboid respectively.

Volume of the cylinder = πr_{1}^{2}h, where r and h_{1} are the radius and height of the cylinder respectively

Dimensions of the cuboid, l × b × h = 5.5 cm × 10 cm × 3.5 cm

Height of the cylindrical coin, h_{1} = 2 mm = 2/10 cm = 0.2 cm

Radius of the cylindrical coin, r = 1.75/2 cm = 0.875 cm

Let n coins be melted to form the required cuboid.

Volume of n coins = Volume of cuboids

n x πr^{2}h_{1} = l × b × h

n = (l × b × h)/πr^{2}h_{1}

= ( 5.5 cm × 10 cm × 3.5 cm) / (22/7 × (0.875 cm)^{2} × 0.2 cm

= (5.5 cm × 10 cm × 3.5 cm × 7) / (22/7 × 0.875 cm × 0.875 cm × 0.2 cm)

= 400

Therefore, the number of coins melted to form such a cuboid is 400

**Video Solution:**

## How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.3 Question 6 :

How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

The number of silver coins each having a diameter of 1.75 cm and thickness of 2 mm required to be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm is 400