Even if I had time I doubt I would have bothered to proceed past $l=4$ or $l=5$. Thus, the unit of volume of the prism is given as V (square units) × (units) cubic units. I could continue, but since this is a contest problem I probably would have taken a chance on $(12,9,2)$ pretty much as soon as I acquired it. Permutation of our previous solution (and not even the optimal one, at that!). Given the surface area, length and width find the height, volume and diagonal of a rectangular prism. Vh lw Correct me asked by Pablo 26 answers How do you know answered by Pablo No, its C D gives you the number for length and width multiplied together. S 2 (lw + lh + wh) d (l 2 + w 2 + h 2) 2. Since $p,q>2$, our choices are $(p,q)\in\$. What is the The formula Vlwh is used to calculate the valume of a rectangular prism. So for a fixed value of $l$, $150+l^2$ must admit an integral factorization $pq$ with $p,q>l$. Let's rewrite the surface area formula as follows: So how would you do this without code? Well, I'd probably begin an exhaustive search, frankly, but with some efficiency. At least I limit the loops to 75, since the largest single dimension to achieve a surface area of 300 has to be less than that: $(75,1,1)$ gives us a surface area of 302: for h = 1 : 75, Certainly it's not the most efficient but sometimes life calls for quick and dirty solutions. The former has a volume of 200, the latter has a volume of 216. FAQ With this tank volume calculator, you can easily estimate the volume of your container. Example: What is the volume of a prism where the base area is 25 m 2 and which is 12 m long: Volume Area × Length. If we are assuming a fully rectangular prism-right angles all around-then there actually are only two candidates: $(h,w,l)=(20,5,2)$ and $(h,w,l)=(12,9,2)$.
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