The inplates, isosceles triangles of the through shown below, were designed to withstand a fluid force of 5800 lbs. How many cubic feet can the tank hold without exceeding this limitation? So the first thing we're going to do is we're going to figure out what this line, this diagonal line is. So if we think about how far up we went, we went up 11 and to the right six because the whole distance across was 12, so Y would equal 11 / 6. The slope of this diagonal line times X. If I wanted to solve for X, I'd cross multiply get 6Y equal 11X or 6 / 11 Y equal X. Now because this is actually a distance of two XI, have X to the right and another X to the left and multiply each side by two and get 12 / 11 Y equaling 2X. So the force is going to equal the depth, in this case zero to D the liquid remember is 0 to however high it goes. In this case, the D, the 62.4 is the density, the 12 elevenths Y is the 2X distance here the d -, y, So the D minus the Y height at each level that we're going times the DY. So we're going to have 62.4 times the 12 elements coming outside. I'm going to distribute the Y times the D and get d * y and the Y times the negative Y and get negative y ^2 d Y. So 62.412 elevenths. If I take the integral and evaluate it, I get d ^2 y ^2 -, 1/3 Y cubed D over or from zero to DD. I'm going to stick in because it's a constant. That depth is going to be a constant. So if I stick in the depth D, I'm going to get 62.412 elements d ^3 / 2 -, d ^3 / 3. The second parenthesis here is going to turn into 3D cubed minus two d ^3 / 6, or just AD cubed over six. The six in that 12 are going to reduce, and we're going to get 2 elevenths d ^3. So 12 elevenths times 1/6 is 2 elevenths d ^3. Now we're told that that's going to be the fluid force that the that the plate can take is 5800. So we're going to take that 62.4 * 2 elevenths D cubed and equal the 5800 to find the depth. So the D is going to equal the cube root of the 5800 * 11 divided by 62.4 * 2 and that's going to be approximately 7.9959. Now the directions tell us not to round till the end. So I'm going to use this exact in my calculator. So the volume is going to be 1/2 base height times the length. So the volume is 1/2. The base was that twelve 11th D and the height is D times the 30, so 1046. So if we look up here, there's my 1046.