A cup has a 5-cm diameter bottom. 7-cm diameter top, and has a height of 9-cm. The volume of the can be approximates by cutting it horizontally into sections exactly with a height if 0.5 cm approximating each section with a cylindrical disk. Then summing the volumes of the disks.

What is the Volume?
Thank you very much for your help!!

Question

A cup has a 5-cm diameter bottom. 7-cm diameter top, and has a height of 9-cm. The volume of the can be approximates by cutting it horizontally into sections exactly with a height if 0.5 cm approximating each section with a cylindrical disk. Then summing the volumes of the disks.

What is the Volume?
Thank you very much for your help!!

mathstudent55 · Answer

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mathstudent55 · Answer

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There are 18 disks.
The bottom one has a lower diameter of 5 cm and an upper diameter of 5 + (7 - 5)/18 cm = 5.1111 cm. The average diameter is (5 + 5.1111) cm / 2 = 5.0555 cm
To find the volume of this disk, treat it like a cylinder with diameter = the average diameter = 5.05555 cm and height = 0.5 cm.
Then do this another 17 times, with the same height every time, and the diameter increasing (7 - 5)/18 cm = 0.1111 cm each time.
Then add all the volumes together.