Question 6 - Converting one shape to another - Chapter 12 Class 10 Surface Areas and Volumes
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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 10 cm 3.5 cm?
Number of coins = ( )/( 1 )
Volume of cuboid
Length (l) = 5.5 cm
Breadth (b) = 10 cm
Height (h) = 3.5 cm
Volume of cuboid =
= 5.5 10 3.5
= 192.5 cm3
Volume of 1 coin
Coin is in shape of cylinder with
Diameter = 1.75 cm
Radius = Diamete /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 = 2
= 22/7 (875/1000)^2 2/10
= 22/7 875/1000 875/1000 0.2
= 0.48125 cm3
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
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 = ( )/( 1 )
= 192.5/0.48125
= 1925/4.8125
= 19250000/48125
= 400
Hence, number of coins = 400
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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