Geometry and Numbers Question

Hi sapp,

your inverted cone is, from a 2D perspective, an isoceles triangle with a base of 5, the water fills a portion of this triangle to have a base of 3.

Based on triangle proportionality, the height of the water is therefore 3/5ths of the height of the total triangle (which is 3) so the h, which is really the remaining height, is the remaining 2/5th's of the height of the triangle, or

2/5*3 = 6/5

for your second question, even though it doesn't look possible, don't panic, break the problem down: the product of 3 digits is 54. in product questions it helps to break down the number into primes: 54 = 2 * 3 * 3 * 3

now it's a 3 digit number bigger than 950, so it's CERTAIN that the hundreds digit has to be 9, which is great cuz it takes care of two of the 3's in 54

now we have a 2 and a 3 left over, but it seems kinda tough, since 923 and 932 are both below 950, so we need to pull a trick out of our sleeve: 1

see even if the number was 92311111111 the product would still be 54, because when you're taking the product (the multiplication) the 1 is basically a neutral value, so use it!

in this case, although we can't make 923 or 932, if we put 2 and 3 together, we get a 6, and 961 fits the bill quite nicely since its big enough, and contains all those pesky primes we've been trying to put together!

(916 woulda worked too, but it's smaller than 950...)

hope that helps!