What is the volume of a cone measuring 1797 centimetres in height and with a base radius of 33.5 centimentres.
411743
The volume of a cone is 1/3 the area of the base of the cone (the circle) times the height.  The area of a circle is pi times the radius squared.\n\nSo, 1/3 (pi)(33.5)(33.5)(1797) = approx. 2,111,865.76 cubic centimeters.
1168044
93.5 sq in\nMultiply by 2.54^2 to get\n603.2246 sq cm
9233
Find the dimensions of the base:\n36 - 4 - 4 = 28\n25 - 4 - 4 = 17\n\nSo the area of the base = 28 x 17 = 476\n\nThe height = 4\n\nSo the volume = 4 x 476 = 1904
85854
A cone holds exactly 1/3 as much as a cylinder with the same radius and height.  So multiply pi times radius squared times height, then divide by 3.
648945
What you wrote isn't a cone. It is the part of the hyperboloid of one sheet x^2+y^2-z^2=1 with z>=0. The intersection with the sphere is a circle on the sphere and so the volume is 0.\n\nIf you *meant* the cone z=sqrt(x^2+y^2), you can evaluate the volume in several ways. I would suggest changing to spherical coordinates, where the equation of both the cone and the sphere are very simple. [rho=1 and phi=pi/4] Don't forget the rho^2 sin(phi) term when integrating!
836396
circumference= 2*r*pi\nwhere r is the radius and pi is approximately 3.14
147975
First, find the volume of the can: [pi]r-squared x the height of the can. If the 3 balls in it each have a radius of 5 cm, then they are each 10 cm tall, and the can is 30 cm tall. So the volume of the can = [pi]x25x30 = 750[pi] cubic cm.\n\nNext, the volume of each ball is 4/3 x [pi]r-cubed, or 166.67[pi] cubic cm. Three of them would be 500[pi] cubic cm.\n\nLast, subtract the volume of the balls from the volume of the cylinder to get 250[pi] cubic cm, or about 785.4 cubic cm.
12258
sorry i made a mistake....this is correct...\ndivide the base by 2.  Now you have a right triangle.  the height is the same, but the base is now 3.  pygathora (spelling, whatever) theorm is A squared + B squared = C squared.  c is the side opposite the right angle, a and b are the other sides.  so 3 squared + 4 squared is 9 + 16 = 25. The square root of 25 is 5, so that is the length of the side.  the volume = area of base times height.  Area of a triangle is 1/2 base times height.  so 3 (one half of 6) times 4 = 12.  times this by height of 8 = 96 cubic units. largest rectangular side is the 6 (the longest side) times 8 = 48 units squared. hope this helped.  the lateral area is the area of the sides added together. so C times 8 = 40 (area of one side)  add the other side of equal area (the C from the second triangle we got when we split the first one) 40 + 40 = 80.  Add the third side of length 6 times 8 = 48.  80 + 48 is 128 (in units squared).  or all sides added up 5 + 5 + 6 = 16 times 8 = 128.
241611
kindly refer to the formula..and do you math HW yourself...\nApart from that if Diameter=8 cm...radius got to be 4cm\n\nI dont know the Surface area formula for cone but should be easy to find it somewhere like google.
866787
let the radius of the cylinder be x,  drawing a cylinder in a cone on the paper, we see 2 triangles - the cone & the triangle with it's base as the top flat surface of the cylinder. follow me?\n\nif u do, then let's assume the height of the second triangle to be y. y can be found in terms of x as:\n(since both triangles are similar)\n\nx:4 :: y:12  \ni.e. x/4 = y/12\n=> y=3x\nthus ht of cylinder = ht of cone - y\n=12-3x\n\nvolume of cylinder = pi*r2*h  (r-> radius, h-> height of cylinder)\nv= pi * x2 * (12-3x) = pi * (12x2 - 3x3)\n  (the second term being 12 *x*x - 3*x*x*x ....sorry, i don't have a math equation display software here)\n\npartialy differentiate above equation wth respect to  x, we then get\ndv/dx = pi * (24*x - 9*x*x)\n\nequating dv/dx to zero, (to find a value of x that makes the volume value either maxium or minimum. u can verify it's max by again differentiating dv/dx with respect to x, equating to zero & finding if the value solved for is positive or negative)\n\nanyways, we get\n\neliminating  pi,\n24*x - 9*x*x=0\n\n=> x=24/9 = 8/3= 2.67\n\nnow, simply substitute this value of x in the volume equatiion above to get\n v= pi * (12*2.67*2.67 - 3*2.67*2.67*2.67)\n= 89.372 or so.\n\n\nuh...i guess i only confused u up, hope it helped u atleast a bit.
822086
The volume is V = pi*r^2*h/3 = 27.  So h = 81/(pi*r^2).\n\nThe amount of paper is the surface area without the base of the cone which is A = pi*r*sqrt(r^2+h^2)  Substitute for h:\nA = pi*r*sqrt(r^2+81^2/(pi^2*r^4))\n= sqrt(pi^2*r^4 + 81^2/r^2)\nSince the square root is an increasing function you can minimize sqrt(f) by minimizing f.  So minimize\npi^2*r^4 + 81^2/r^2\nThis differentiates to\n4pi^2*r^3 - 2*81^2/r^3, which must be equal to zero.\n4pi^2*r^3 = 2*81^2/r^3\n2pi^2*r^6 = 81^2\nr=(81^2/2pi^2)^(1/6).  If my calculations are correct you can figure out h from this...
981841
area of the base times the height.
329292
V=(4/3)*pi*r^3\n\nwhere r is the radius of the sphere and V is volume.
917141
the radius is half the diameter.
877943
volume of cyllinder = area of circle times height\n\n= Pi x radius x radius  x height\n\nremember its just the same as finding the volume of any prism.\nfind the area of the shape of the end then multiply by its length!!
543816
Yes it is !!\n\nFor proof of volume of cone, pls go to :\n\nhttp://mathforum.org/library/drmath/view/53646.html\n\n\nThe following site has got the proof for area of circle :-\n\n\nhttp://64.233.161.104/search?q=cache:FbBn10NweQkJ:www.artofproblemsolving.com/LaTeX/Examples/AreaOfACircle.pdf+area%2Bcircle%2Bproof&hl=en&gl=in&ct=clnk&cd=1
754188
you divide the mass by the volume\n1.2.14 g/cm^3\n2..82 g/cm^3\ngood luck!