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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: VVVCCCEEE on August 13, 2018, 06:44:12 pm

Title: 2 questions
Post by: VVVCCCEEE on August 13, 2018, 06:44:12 pm: Much help needed, thanks
Title: Re: 2 questions
Post by: M909 on August 13, 2018, 06:57:22 pm: For the cone question I would calculate the volume of the original cone, then the volume of the end that has been cut off, then subtract that from the original to get the remaining volume.

For the prism (I'm assuming you want volume?), calculate the trapezoid area with Area = 0.5*(top length + bottom length)*height, then multiply this by the width
Title: Re: 2 questions
Post by: VVVCCCEEE on August 14, 2018, 08:44:31 pm: Could you give me the equation for the cone question. I did 1/3pi(5)^2x30-1/3pi(2.5)^2 x25 but the ans says 782
Title: Re: 2 questions
Post by: S200 on August 14, 2018, 09:37:27 pm: Quote from: VVVCCCEEE on August 14, 2018, 08:44:31 pm
Could you give me the equation for the cone question. I did 1/3pi(5)^2x30-1/3pi(2.5)^2 x25 but the ans says 782
The book's correct.
Full volume of the cone is 785.4, by using the formula, with h(30) and r(5)
$V=\pi r^2 \frac {h} {3}$

Now, where you probably went wrong. The upper part of the cone uses h(5), and the radius has to be ratio'ed back to meet this - You can use similar triangles or Pythagoras, doesn't really matter
$\frac {5} {30} = \frac {1} {6} \\ <br />\therefore \\<br />\text {Radius (r) } = \frac {5} {6}$
So, with that h and r, we get V ≈ 3.64.
Minus this from the first value and you get 781.76, ∴ 782