Question

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

Answer 1

Hi ,

i ) Dimensions of the each silver coin

( cylinder ):

diameter ( d ) = 1.75 cm

radius ( r ) = d/2 = ( 1.75/2 ) cm

thickness = height ( h ) = 2mm =( 1/5 )cm

volume of each coin = V1

V1 = πr²h

= ( 22/7 ) × ( 1.75/2 )² × ( 1/5 )

V1 = 0.48125 cm³ ----( 1 )

ii ) Dimensions of the cuboid :

length ( l ) = 5.5 cm

breadth ( b ) = 10 cm

height ( H ) = 3.5 cm

Volume of the Cubiod = V2

V2 = lbh

= 5.5 cm × 10cm × 3.5 cm

= 175 cm³----( 2 )

according to the problem given ,

Let " n " silver coins melted to form

required cuboid .

n = V2/V1

= ( 2 )/( 1 )

= 175/( 0.48125 )

= 363.636

≈ 364

Therefore ,

364 required to make a cuboid.

I hope this helps you.

: )