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.
How do you find the volume of a prism and a cylinder?.How to find the surface area of Rectangular Prisms:įind the area of two sides (Length*Height)*2 sides.įind the area of adjacent sides (Width*Height)*2 sides.įind the area of ends (Length*Width)*2 ends.Īdd the three areas together to find the surface area. How do you find the surface area of a prism?.For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. To find the area of a triangle, multiply the base by the height and then divide by 2. How do you measure the surface area of a triangle?.The answer is the surface area of the above triangular prism is 486 square inches.
Then, multiply the sum of the triangle sides by the height of the prism (H) and add the values together for the answer, making sure to include the appropriate unit of measurement.