UPSC CDS 2 2021 Math Paper

Given, dimensions of silver coins (cylindrical shape)
Thickness (h1)=4mm
=‌

4

10

cm=0.4cm
Diameter =3.5cm
1∴ Radius, r=‌

3.5

2

=1.75cm
And dimensions of cuboid are
21cm×11cm×7cm
i.e., I=21cm,b=11cm and h2=7cm
Let n number of coins are melted to form a cuboid.
In such case, volume will remain same.
∴ Volume of n coins = Volume of cuboid
⇒n×V‌one coin ‌=V‌cuboid ‌
⇒n×πr2h1=I×b×h2⇒n=‌

1⋅b⋅h2

πr2h1

⇒n=‌

21×11×7

22 7 ×(1.75×1.75)×0.4

⇒n=‌

21×7×7

2×(‌ 7 4 ×‌ 7 4 )×(‌ 4 10 )

n=‌

21×4×4×10

2×4

=21×2×10=420
Hence, 420 silver coins must be melted to form a cuboid.