Question

A metallic cylindrical bar of length 18cm and base radius 2cm is melted and recast
into a solid cylinder of base radius 3cm . find :
a) the height of the new cylinder
b) the ratiof the total surface area of the bar to that of new cylinder.
Plz answer fast and step by step​

Answer 1

Step-by-step explanation:

For cylindrical bar

h = 18cm , r = 2cm

Volume of cylinder = πr^2h

= π(2)^2 × 18

= π × 4 × 18

= 72 π

( a )Volume of new cylinder = Volume of first cylinder

π (3)^2 × h = 72 π

here, π gets cancelled

9 × h = 72

h = 72 ÷ 9

h = 8cm

Therefore, height of new cylinder is 8 cm .

Total surface area of cylinder = 2πr ( r + h )

= 2π × 2 ( 2 + 18 )

=2π × 40

= 80π

Total surface area of new cylinder = 2πr(r + h )

= 2π × 3 (3 + 8 )

= 2π × 33

=66π

( b ) ratio = TSA of cylinder

TSA of new cylinder

= 80π

66π

= 40

33

= 40:33

Therefore ,ratio of the total surface area of the bar to that of new cylinder is 40:33.

Hope this helps!!