![]() of a prism is the area of its cross-section multiplied by the length. The volume close volume The amount of space a 3D shape takes up. ![]() Surface area is measured in square units, such as cm² and mm². shapes and the area of different shapes helps when working out the surface area of a prism. Measured in square units, such as cm² and m². of 3D close surface area (of a 3D shape) The total area of all the faces of a 3D shape. Understanding nets close net A group of joined 2D shapes which fold to form a 3D shape. The number of rectangular faces is the same as the number of edges close Edge The line formed by joining two vertices of a shape. at either end of the prism and a set of rectangles between them. faces close face One of the flat surfaces of a solid shape. is made up of congruent close congruent Shapes that are the same shape and size, they are identical. The surface area close surface area (of a 3D shape) The total area of all the faces of a 3D shape. The cross-section is a polygon close polygon A closed 2D shape bounded by straight lines. has a constant cross-section close cross-section The face that results from slicing through a solid shape. Thus, the point we have found is a local minimum.A prism close prism A 3D shape with a constant polygon cross-section. ![]() The second derivative of this guy is strictly positive for positive s, implying the function is concave up for positive s. To do so you must take the second derivative. We'll end up with h = 2 * 5 2/3 *7 1/3 / sqrt(3).ĮDIT: It's a bit pedantic, but technically you have to make sure that it's a local minimum at the value of s that I've found. From there, we can easily find the height by substituting into our previous formula. We want to find the minimum so we set SA' = 0. SA = 2(sqrt(3)/4)s 2 + 3sh (the first term is the 2 triangular parts and the second term is the three lateral, rectangular parts).Īs a function of s alone, we have SA = 2(sqrt(3)/4)s 2 + 4sqrt(3)350/s. This is equivalent to h = 4*350/(sqrt(3)s 2 ). V = (sqrt(3)/4)hs 2 = 350 cm 3 (I converted mL to cm 3 for ease). Then the area of the base is (sqrt(3)/4)s 2. Let s be the base of the triangle and h be the height. This is an ordinary optimization problem so it requires the use of basic calculus. Re-read your post before hitting submit, does it still make sense. ![]() Show your work! Detail what you have tried and what isn't working.Use proper spelling, grammar and punctuation.Give context and details to your question, not just the equation.Help others, help you! How to ask a good question Asking for solutions without any effort on your part, is not okay. Beginner questions and asking for help with homework is okay. Post your question and outline the steps you've taken to solve the problem on your own. Do not use ChatGPT in a question or an answerĭon't just post a question and say "HELP".Do not solicit or offer payments to complete your assignments or tests.No cheating - do not post questions from exams, tests, midterms, etc.No post flooding - Limit your posts to 2 or 3 questions a day.Don't be a jerk - don't be obnoxious or rude.Homework policy - asking for help is okay, asking to be given the solution is not.Make your question clear and concise - include steps you have tried.Stay on topic - this subreddit is for math questions no how-to guides, or non math related questions.Explain your post - show your efforts and explain what you are specifically confused with.
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