UPSC CDS 2 2019 Math Paper

We have,
A cylinder height = 10 cm and radius is 6 cm.
Volume of a solid cylinder ‌=πr2h
‌‌=π×62×10
‌‌=360π
Flat surface area of cylinder =2πr2=2π×62=72πcm2
A solid cylinder is melted into two cones with same height 10cm.
The ratio of volume of two cone is 1: 2 .
Means if we divide 360π into 1: 2 then 120π:240π
So one cone volume is 120π and second has 240π.
∴ Cone volume =‌

π

3

r2h
Then first bigger cone has R radius. then 240π=‌

π

3

R2h⇒R2=72
Then flat surface area of first cone =πR2=72π
Then second smaller cone has r radius. then 120π=‌

π

3

r2h⇒r2=36
Then flat surface area of second cone =πr2=36π
Total surface area of cone =72π+36π=108π
So flat surface area from cylinder to cone is increased by 36π which is 50 % increase.