1 / 9

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.

vaughan-johns
Télécharger la présentation

Cylinders

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related