![]() ![]() ![]() But how do we figure out this height? Well, this is where One half times the base 10 times the height is. So, if we can figure that out, then we can calculate what But what is our height? Our height would be, let me do this in another color, our height would be the length Our base right over here is, our base is 10. That the area of a triangle is equal to one half times Recognize, this is an isosceles triangle, and another hint is that Solving this equation for y, we see that y = sqrt( 9 - 9/16*x 2 )īut, if we graph out the ellipse, we can see that the coordinate "y" is only half of the total length of the hypotenouse.And see if you can find the area of this triangle, and I'll give you two hints. V = integral of ( 1/4 * d ^ 2 ) from (x=-4) to (x=4) dxīut we still need to express the length of the hypotenuse of our triangle, d, in terms of the parameter that we are integrating, in this case that parameter is x. ![]() The bounds of our integral x1 and x2 we can find by just plugging in y = 0 to our elliptical formula and getting x=-4 and x=4. V = integral of ( 1/4 * d ^ 2 ) from (x=x1) to (x=x2) dx Because our triangles lie perpendicular to the x-axis, we need to integrate the area along the x-axis to find the volume. The volume of any solid with a cross section of an isosceles right triangle is just the integral of that area along the length of that solid. The area of an Isosceles right triangle is, when given the length of the diagonal, d, just equal to Pastebin / / IDEOne Revert to older template If you have trouble with spacing, add some blank spaces with įor more commands, please see User Moderation Please contact u/Oryv if the bot malfunctions, or if you have questions on how to use it. Simply mention the bot in a comment and put the expressions that need to be rendered in code blocks, and u/LaTeX4Reddit will respond. To use LaTeX on this subreddit, use u/LaTeX4Reddit. Accept answers at your own risk.įor citation questions, check the Purdue Online Writing Lab Keep in mind that we do not and will not have any sort of vetting procedure for responders. This includes asking for "likes," page views, or similar things. Offers or solicitations of payment in any form. Requests for help with cheating, plagiarism, or other violations of academic integrity violations of copyright or terms of use or other illegal or unethical activities. Posts tagged "urgent," "ASAP," "important," "due in an hour," etc. "Do this for me" posts such as posting of quizzes or lists of questions. When your question has been answered, please edit the post's flair to " ✓ Answered".Ĭopied questions without context or explanation. What does your instructor want you to accomplish? Still acceptable…, but preferably not: Grade 1-6 (Pri) Grade 7-10 (Sec) Grade 11-12 (Pre-Uni) University/College ❗️ READ THE RULES BEFORE POSTING
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