The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it ?
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Let the radius of the cylindrical vessel = r cm
From question, h = 1 m = 100 cm and volume = 15.4 litre = 15.4 × 10^3 cm^3 [because 1 litre = 10^3 cm^3]
From formula, volume of cylinder = pi × r^2 × h cm^2
Therefore, 15.4 × 10^3 = 22/7 × r^2 × 100
or r^2 = 15.4 × 10^3 × 7 / 22 × 10^2
= 15.4 × 10 × 7 / 22
= 154 × 7 / 22
= 7 × 7
= 7^2
Therefore, area of metal sheet required = curved surface area of cylinder + area of both circular ends
= 2 × pi × r × h + 2 × pi × r^2
= 2 × pi × r × (h + r)
= 2 × 22/7 × 7 × (100 + 7)
= 44 × 107
= 4708 cm^2
= 4708 / 100 × 100 m^2 [because 1 cm = 1/100 m]
= 0.4708 m^2
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Let the radius of the cylindrical vessel = r cm
From question, h = 1 m = 100 cm and volume = 15.4 litre = 15.4 × 10^3 cm^3 [because 1 litre = 10^3 cm^3]
From formula, volume of cylinder = pi × r^2 × h cm^2
Therefore, 15.4 × 10^3 = 22/7 × r^2 × 100
or r^2 = 15.4 × 10^3 × 7 / 22 × 10^2
= 15.4 × 10 × 7 / 22
= 154 × 7 / 22
= 7 × 7
= 7^2
Therefore, area of metal sheet required = curved surface area of cylinder + area of both circular ends
= 2 × pi × r × h + 2 × pi × r^2
= 2 × pi × r × (h + r)
= 2 × 22/7 × 7 × (100 + 7)
= 44 × 107
= 4708 cm^2
= 4708 / 100 × 100 m^2 [because 1 cm = 1/100 m]
= 0.4708 m^2
_____________________
HOPE IT HELPS ❤❤