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Ex 13.3, 6 - How many silver coins, 1.75 cm in diameter - Conversion of one shape to another


 

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.3, 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 × 10 cm × 3.5 cm? Number of coins = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑢𝑏𝑜𝑖𝑑)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑐𝑜𝑖𝑛) Volume of cuboid Length (l) = 5.5 cm Breadth (b) = 10 cm Height (h) = 3.5 cm Volume of cuboid = 𝑙𝑏ℎ = 5.5 ×10×3.5 = 192.5 cm3 Volume of 1 coin Coin is in shape of cylinder with Diameter = 1.75 cm Radius = Diamete𝑟/2 = 1.75/2 cm= 0.875 cm = 875/1000 cm Height = 2 mm = 2 × 1/10 cm = 2/10 cm Volume of 1 coin = 𝜋𝑟2ℎ = 22/7×(875/1000)^2× 2/10 = 22/7×875/1000 ×875/1000×0.2 = 0.48125 cm3 Number of coins = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑢𝑏𝑜𝑖𝑑)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑐𝑜𝑖𝑛) = 192.5/0.48125 = 1925/4.8125 = 19250000/48125 = 400 Hence, number of coins = 400

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