Question

6 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 x 10 cm x 3.5 cm?​

Answer 1

Answer:

Step-by-step explanation:

Dimensions of one silver coin

Diameter = 1.75 cm

∴ Radius =            Diameter            

                                      2

$\sf Radius = \sf \dfrac{1.75}{2} = \dfrac{175}{200} = \dfrac{7}{8} = 0.875 \;cm.$

Thickness (Height) = 2mm

$\sf2mm = \dfrac{2}{10} cm$

Dimensions of Cuboid

Length(l) = 5.5 cm

Breadth (b) = 10 cm

Height (h) =  3.5 cm

Volumes

Cuboid

Volume of cuboid = lbh

Volume = 5.5 cm x 10 cm x 3.5 cm

Volume of cuboid = 192.5 cm³

1 Coin

Coin is in the shape of a cylinder

Volume of  cylinder = π × r²×h

 Put,

π = 22/7

r = 875/1000

h = 2/10

$\sf Volume = \sf \dfrac{22}{7} * \dfrac{875}{1000}*\dfrac{875}{1000} *0.2$

Volume = 0.48125 cm³

$\sf Number \;of \;coins \:required \:to\: form \:a \:cuboid = \dfrac{Volume\; of\; the \;cuboid}{Volume \:of \:one \:coin}$

$\implies \dfrac{192.5}{0.48125}$

$\implies \dfrac{19250000}{48125}$

= 400 Coins