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Cylinders

Cylinders. Exercise1:. 10cm. Cylinders. 7cm. For a cylinder with a height of 10cm and a radius of 7cm, find:. (i) The volume of the cylinder. (i) The total surface area of the cylinder. Solution:. Step1: Imagine the cylinder as a stack of circles. 10cm.

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Cylinders

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  1. Cylinders

  2. Exercise1: 10cm Cylinders 7cm For a cylinder with a height of 10cm and a radius of 7cm, find: (i) The volume of the cylinder. (i) The total surface area of the cylinder.

  3. Solution: Step1: Imagine the cylinder as a stack of circles. 10cm Step2: The volume is given by the area of one of these circles multiplied by the height of the cylinder. Cylinders 7cm Volume, V = r²h => V = (22/7)(7²)(10) => V = 1540cm³ Step3: Imagine the cylinder as 2 circles and a stretched out curved surface. Total surface area, TSA = 2rh + 2r² => TSA = 2(22/7)(7)(10) + 2(22/7)(7²) => TSA = 440 + 308 => TSA = 748cm²

  4. Exercise2: 40cm Cylinders 10cm 12cm 3cm A cylindrical jug full of water has a radius of 12cm and is 40cm tall. Water from it is poured into cylindrical glasses of diameter 3cm and height 10cm. How many such glasses can be filled?

  5. Solution: Step1: Find the volume of the jug 40cm V = r²h Cylinders => V = (22/7)(12²)(40) 10cm => V = 18103cm³ 12cm 3cm Step2: Find the volume of the glass. V = r²h => V = (22/7)(3²)(10) => V = 283cm³ Step3: Divide the volume of the jug by the volume of the glasses. No. of glasses = 18103 / 283 => No. of glasses = 64

  6. Exercise3: CSA = 660cm² Cylinders 10cm The curved surface area of a cylinder is 660cm². If the diameter of the base is 10cm, calculate its height and its volume.

  7. Solution: Step1: Find the radius of the base of the cylinder. Radius = 5cm. CSA = 660cm² Cylinders Step2: Find the height. Remember the CSA is 660cm². => 2rh = 660 => 2(22/7)(5)h = 660 10cm => 2(22/7)(5)h = 660 => 31h  660 => h  21 => Height = 21cm Step3: Find the volume Volume, V = r²h => V = (22/7)(5²)(21) => V = (22/7)(25)(21) => V = 1650 => Volume = 1650cm³

  8. Exercise4: Cylinders 16cm h = 8cm 6cm The volumes of these cylinders are equal. Find the missing dimension, h.

  9. Solution: Volume of cylinder = r²h Volume1 = Volume2 16cm Cylinders h => (22/7)(8²)(h) = (22/7)(6²)(16) = => (22/7)(64)(h) = (22/7)(36)(16) 6cm 8cm Cylinder1 Cylinder2 => 201h 1810 => h 9 => Height of cylinder1  9cm.

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