Assume that the volume of the mountain to start above sea level and the peak of the mountain to be a right circular cone.
205429
volume for a cone (Mt. Everest) is: 1/3Bh (1/3 X Area of base X height). Find that and you might be able to find the mass.
649885
The volume of a cylinder equals the (area of the base)*height = π r2h
670245
Its usually known as a frustum . Think of it as an upturned Bucket , essentially , top part of the a  cone cut off by a plane perpendicular to the axis .
310313
Assuming you're putting the same volume of water in each, set the volumes of the cylinders equal and solve for the hight of the stout pipe.
2812
A point does not have a direction. So I guess the answer is yes.
76407
The distance around it.The circumference.
575836
A cone is, as you correctly state, a surface of revolution.  You can think of it as the volume enclosed in three-dimensional space by rotating a straight line passing through the origin around the x-axis.\n\nNow, because the straight line passes through the origin and rotates all the way around the x-axis to form the surface of the cone, at some point during its revolution, it must be in the plane formed by the x and y axes.  When it is, we can write its equation in two dimensions like this:\n\ny = mx + c\n\nBecause the line passes through the origin, c=0, so the equation becomes:\n\ny = mx         (equation A)\n\nNow for the calculus.  \n\nConsider a very small segment along the line.  As the line rotates, the tiny segment sweeps out a nearly-cylindrical volume symmetrical about the x-axis.  As the length of the segment tends towards zero, the volume it sweeps out becomes closer and closer to a cylinder.\n\nLet the distance on the x-axis corresponding to the line segment be dx.  What is the volume of the cylinder swept out at a particular point on the x-axis?\n\nWell, the volume of a cylinder is given by:\n\nV = pi * r^2 * h\n\nwhere r is the radius of the cylinder and h the height.  We know that the height of the cylinder is dx.  What about its radius?  This is given by the y-coordinate of the point where the cylinder touches the line.  We can determine this from equation A above: the radius is mx.\n\nSo the volume (call it dV) of this very thin cylinder is given by\n\ndV = pi * (mx)^2 * dx\n\nTo find the volume of the whole cone, let its height, measured from tip to base along the axis of symmetry (the x-axis, remember), be H.  Now to find the total volume we need to add up all the different dV's along the x-axis from 0 to H.  In calculus, this is called integration and is normally represented by a sign like a big old-fashioned letter S.  I can't write that here, but here goes:\n\nV = Integral from 0 to H (dV)\n= Integral from 0 to H (pi * (mx)^2 * dx)\n= pi * m^2 * Integral from 0 to H (x^2 dx)\n= pi * m^2 * 1/3 * (H^3 - 0^3)\n= pi * m^2 * 1/3 * H^3\n\nTo find the volume of a truncated cone, instead of integrating from 0 to H, choose H1 and H2 so that H2>H1 and integrate between them, giving\n\nV(truncated) = pi * m^2 * 1/3 * (H2^3 - H1^3)\n\nIf your problem is stated in terms of the radii of the ends of the truncated cone and its height, choose m, H1 and H2 so that \n\nm*H1 = r1 = radius of smaller end\nm*H2 = r2 = radius of larger end\nH2-H1 = H = height of truncated cone\n\nThis gives you three simultaneous equations in three variables which you can easily solve:\n\nm*(H2-H1) = r2-r1\nm*H = r2-r1\nm = (r2-r1)/H\n\nm*H1 = r1\n((r2-r1)/H)*H1=r1\nH1 = r1*H/(r2-r1)\n\nsimilarly\n\nH2 = r1*H/(r2-r1)\n\nSo the volume is given by\n\nV = pi * m^2 * 1/3 * (H2^3 - H1^3)\n\nsubstituting in the solutions and simplifying, we get:\n\nV = 1/3 * pi * H * (r2^3-r1^3)/(r2-r1)\n\nAs a quick sanity check, let r1 be zero and r2 be R.  We get\n\nV = 1/3 * pi * H * R^2\n\nwhich from high school geometry we know is the formula for the volume of a cone with height H and base radius R.\n\nThis would have been easier to explain with diagrams, so I hope it makes sense!
270108
Volume of a cone is one-third the area of the base (a circle with a radius of three) times the height.\n\nFor slant height, think Pythagorean Theorem. Think of a cross section of the cone and draw a line for the height (down the middle) and a line for one radius. You would have two legs of a right triangle, with the hypoteneuse being the slant height. \n\nFor lateral area (that's the surface area of the slanted surface, the formula is pi x radius x slant height. (Sometimes it's given as 1/2 the circumference of the base times the slant height, but that's really the same thing as the formula I gave you.)\n\nHope that helps.
416296
The maximum height is given by the point where the slope (derivative) is zero.\n\nh'(t) = -32t + 96 = 0\n32t= 96\nt = 3\n\nSo the maximum point will be at time t = 3.\n\nh(3) = 5 + 96(3) - 16(3)²\nh(3) = 5 + 288 - 16*9\nh(3) = 293 - 144\nh(3) = 149 ft.\n\nNow just don't stand directly underneath this when the arrow returns to Earth!
6589
About 6 inches of natural snow base.
528437
Hiking sounds like a great idea.
363578
the hight of the first prisim is greater remember the equasion l*w*h=V
505579
I can't find anywhere that says exactly on this.  However I could find that it tops out at about 600m above the surrounding planes.  Also it is aprox 3000m in diameter.  So if it is a perfect cone, which it is not, it would be 14,681,680 square meters surface area.  Not sure how much this helps you.
530272
yes, so that it can maintain as close as possible it's position above a specific geophraphical area as the world spins.
36906
shape it into a brick divide its mass by its volume
368981
The fact that he took his return trip later just complicates the problem. The question can be restated as one person leaves from the top of the mountain and one person leaves from the bottom of the mountain. They leave at the same time. Explain why, if they follow the same path, they will run into each other each other at some point. Stated this way, it is obvious, right?\n\nIf you want a more rigorous solution, here you go. This is a continuity question. Let f(t) denote the distance *from the bottom of the mountain* at time t on the trip up the mountain and let g(t) denote the distance *from the bottom of the mountain* at time t. Change your units so that your time starts at zero (so 8AM is t=0) and you make it up the mountain in time 1 (so 1PM is t=1) and your distance from the bottom to the top of the mountain is 1. With this set up, g(x) lies in the interval [0,1] for every x in the interval [0,1], and the same holds for f(x). Consider the function g(t)-f(t). The physical interpretation makes it clear that f(t) and g(t), hence g(t)-f(t), are continuous functions of t; that is, you don't just disappear at one point and reappear at another point without having travelled through every point in between. g(0)-f(0)=1-0=1>0 and g(1)-f(1)=g(1)-1<=0. The intermediate value theorem tells you that there is some time t_0 such that g(t_0)-f(t_0)=0. That is, there is some time t_0 such that g(t_0)) = f(t_0). Your deja vu moment happens at time t_0.
115762
Form a triagle. Cut the "corners" off.