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# how to find volume of a trapezoidal prism

Question:So there is a big triangular prism & a small one. The height of the big one is 8 yd & the small one 4 yd. Nothing else is given except the big prism's volume, which is 88 yd. How can I find the volume of the small prism? They are also proportional!

Answers:letters in UPPER CASE are variables set for the BIG prism, while letters in LOWER CASE are variables set for the SMALL prism. volume of triangular prism = 1/3 * area of the base * height = 1/3 (1/2 ab) * height set ab as a constant K volume = 1/6 *K*height V=88; H=8 substituting, 88=1/6 * K * 8 K = 66 (sub this to get the small prism's vol) v=1/6 * 66 * 4 v=44

Question:If I am given a trapezoid in the shape of a gutter: \___/, where the top is the water, how do I calculate the volume of the water in relation to the depth H? In other words, I have a 3D trapezoid that I need to find the volume of, but I only know the length of the sides and bottom; the top changes. I believe it has something to do with Riemann Sum, but I cannot find out exactly how to answer this question. Any help is greatly appreciated!

Answers:If your shape is like a gutter with 2 flat sides on either end, I would find a formula for the area of the trapezoid cross-section of the water in the gutter. If you have a formula for the area of the cross-section, you can just multiply it by the length of the gutter. Again though, this is assuming a flat-ended gutter with the trapezoid cross-section.

Question:This is my question A water trough is 8 m long and its cross-section is an isosceles trapezoid which is 80 cm wide at the bottom and 160 cm wide at the top, and the height is 40 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm^3, when the depth of the water is d cm. I have tried several things but could not come up with the correct answer, I am on my last try as it is an online learning tool, thanks in advance for any help. P.S. Not sure if this will help but I have inputted several answers, this being the closest to the answer as far as I think, (800*d^2)+(1600*d^2), not sure if that is any help, but thanks again.

Answers:The volume of a prism is the product of the area of the base and the height of the object. In this case, the base would be the trapezoid cross-section and the height would be 8m (or 800 cm) The area of a trapezoid is 1/2 * (b1 + b2) * h, where b1 is the first base, b2 is the second base (let's say that this base is 80 cm), h is the height (in this case represented as d) Now, we can represent d as a linear function of the 2 bases When b1 = 160 cm, d = 40 cm When b1 = 80 cm, d = 0 cm 160 = m * 40 + t 80 = m * 0 + t 80 = t 160 = 40m + 80 80 = 40m 2 = m b1 = 2d + 80 Now, the volume of our trough is: V = (1/2) * (b1 + b2) * h h = d b2 = 80 b1 = 2d + 80 V = (1/2) * (2d + 80 + 80) * d V = (1/2) * (2d + 160) * d V = (d + 80) * d V = d^2 + 80d That's as far as we can go for now.

Question:I have a math test tomorrow and need some help understanding 2 concepts. 1. How do you find the surface area of a Right, Right triangular prism. For example, if the height is 6 feet, the base is 8 feet and the length is 15 feet, what is the surface area. 2. How do you find the volume of a trapezoidal prism? For example, if the upper base of the trapezoid is 5 feet, the lower base of the trapezoid is 2 feet, the height of the trapezoid is 3.5 feet and the length of the prism is 12 feet, what is the volume?

Answers:// 1) the base area is 24 total surface area=2*24+6*15+8*15+10*15=408sqft