2015年12月17日 · Formula for Volume of a Trapezoidal Prism. If the prism length is L,trapezoid base width B, trapezoid top width A, and trapezoid height H, then the volume of the prism is given by the four-variable formula: V(L, B, A, H) = LH(A + B)/2. In other words, multiply together the length, height, and average of A and B.

2018年5月9日 · Use the formula for the volume of a triangular pyramid: V = 1/3Ah, where A = area of the triangular base, and H = height of the pyramid. Let's take an example triangular pyramid and try this formula out. Let's say the height of the pyramid is 8, and the triangular base has a base of 6 and a height of 4. First we need A, the area of the triangular base. Remember …

How do you find the volume of the solid with base region bounded by the curve #9x^2+4y^2=36# if cross sections perpendicular to the #x#-axis are isosceles right triangles with hypotenuse on the base? How do you find the volume of the solid with base region bounded by the triangle with vertices #(0,0)#, #(1,0)#, and #(0,1)# if cross sections ...

The molar volume of a gas is derived from the ideal gas law #PV = nRT#: #PV = nRT -> V = (nRT)/P -> V/n = (RT)/P# Let's say you were given a temperature of 355 K and a pressure of 2.5 atm, and asked to determine the gas' molar volume at these conditions. Since molar volume refers to the volume occupied by 1 mole, you'd get

The volume of a solid of revolution can be determined by integrating the area of the circles created by the revolution. For a function rotated about the x-axis, the volume is given by \\pi \\int_a^b f^2(x) dx.

2014年10月17日 · The volume v of a sphere in terms of pi is v = 4/3pir^3 why does it need to be multiplied by 4/3? the formula was based from calculus. Since the question is under pre-calculus, best accept it as a fact for now.

2014年9月21日 · If you have a cross-sectional area function A(x) of the solid that spans from x=a to x=b, then you can find the volume V by V=int_a^b A(x)dx, which can be expressed as the limit of the right Riemann sum =lim_{n to infty}sum_{i=1}^infty A(a+iDeltax)Delta x, where Delta x={b-a}/n

2016年8月19日 · Assuming we want to find how much base should be added to an acid with a known concentration. In the question, it should be provided the following data: Concentration of the acid: #M_a#. Volume of the acid: #V_a# Concentration of the base: #M_b# and we will need to determine the volume of the base (#V_b#) needed to titrate the acid.

2016年7月2日 · = 29/30 pi Consider the small element width dx as shown, being revolved around the line x = -1 The cross sectional area (csa) of the washer of width dx is the csa of the outer circle minus the csa of the inner ie dA = pi (1 + x + dx)^2 - pi (1 + x)^2 simplify the algebra with u = 1+ x so we have dA = pi ((u+dx)^2 - u^2) = pi (2u dx + dx^2) = pi (2 (1+x) dx + dx^2) we can …

2014年8月30日 · If the radius of its circular cross section is r, and the radius of the circle traced by the center of the cross sections is R, then the volume of the torus is V=2pi^2r^2R. Let's say the torus is obtained by rotating the circular region x^2+(y-R)^2=r^2 about the x-axis. Notice that this circular region is the region between the curves: y=sqrt{r^2-x^2}+R and y=-sqrt{r^2-x^2}+R. By …