Volumes and solids and revolutions, worded explenations

[Halil]

HI guys,

I need help with volume questions. There are a few questions asked in a type which is not explained in my book.

Here it is (example): Find the volume of a truncated cone of height 10cm, a base of radius 5cm and a top radius of 2cm.

Rather then showing me how to solve this one, can someone tell me what the values will represent in my graph, or preferably can someone show me a graph with such information.


Any help will be appreciated

[brightsky]

since your cone has a base radius of 5cm and a height of 10cm, then you know that the graph goes past point (10,5). since it's a cone we're talking about, it goes past (0,0) as well. so you have a linear graph of: y = 1/2 x. now since it's truncated, and you know that top radius is 2cm (sub this into the graph to work out x value), then you know that the domain we're going to look at is restricted to [4, 10]. rotate this around the x-axis to work out your volume.

[moekamo]

a truncated cone is a cone with the top sliced off, so your graph will be linear as shown in the attached pic. Note that you could have the 5 and 2 swapped around and you would get the same result.

[Halil]

you guys are legends thanks

[Halil]

moekamo, if my question is, lets say a spehere, would the heigt, radius represent the same lines as the grapgh you just showed?
WOuld it be okay if you can show me an example with a cylinder and a sphere and which line represents which info, please

[moekamo]

nooo, they'de be completely different. in the attached pics, the cylinder is a horizontal line y=r rotated about the x axis from 0 to h. Alternatively you could do it by rotating about the y axis, see if you can figure out the graph for this one.

For a sphere, you just rotate a semicircle of radius r about the x axis, like in the second pic.