Magical Extra Credit (10 points) You may use a calculator to compute the integra

Question

Magical Extra Credit (10 points) You may use a calculator to compute the integrals. IHowever, you must set up the integrals yourself without help from a website (T' know if you did) For the folowing draw the graph, a picture of the 3 dimenional object, a find the volume described Du the work on yourwn peice of paper. I expect the work to be meat, clean and clear Yon may work together, bt must complete your own write up, and cite the people person yot workad with. 1) THE WAND A wand is needed to start the adventure. Find the volume of a wand that is created by rotating .5x along the x axis from 2) THE POTION BOTTLE lhe potion bottle is the shape bound betwoon the graphs f(x)--9(z-5)2 + 6 and g(r) = 27x3 Use the she method to find the volumc of the object created when the area between the graphs is rotated about the y axis. 3) THE WIZARDS HAT The wizards ha s dcibed by the following g(z)--2(4). Find the volume of the when it' is roaod along the y-axis using the cylindrical method Also, I want my hat to have a brin more of a witches hat) Add to the hat a brim that has a width of 2 (assume the brim has width .) Ilint: What is the radius of the bottom of the wizards hat?) Draw a picture 4) THE RING

Explanation / Answer

1)volume of wand =integral[0 to 5] pi *(0.5x)^2 dx

=integral[0 to 5] 0.25pi x^2 dx

=[0 to 5] 0.25pi (x^3)/3 +c

=0.25*pi*(5^3 -0)/3

=125*0.25*pi/3

=10.42 pi

=32.7

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