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 according to the given question.
From the figure, it can be seen that the shape of the silver coin is cylindrical.
As we know that the silver coins are to be melted and recast into a single solid cuboid. Therefore the cuboid formed by recasting these coins will have the same volume equal to 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 solids 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 = πr2h₁, where r and h₁ 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, h₁ = 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 cuboid
n x πr2h₁ = l × b × h
n = (l × b × h)/πr2h₁
= ( 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 × 0.875 cm × 0.875 cm × 0.2 cm)
= 400
Therefore, the number of coins melted to form such a cuboid is 400.
☛ Check: NCERT Solutions Class 10 Maths Chapter 13
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
Summary:
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.
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