To use the wave function for a particle in a box to calculate the probability that the particle is found in various regions within the box. The quantum mechanical probability that a particle described by the (normalized) wave function ψ(x) is found in the region between x=a and x=b is P=∫ba|ψ(x)|2dx. The specific example of a particle trapped in an infinitely deep potential well, sometimes called a particle in a box, serves as good practice for calculating these probabilities, because the wave functions for this situation are easy to write down. If the ends of the box are at x=0 and x=L, then the allowed wave functions are ψ(x)={2L−−√sin(nπxL),0, for 0≤x≤L, for all other x, where n=1 is the ground-state wave function, n=2 is the first excited state, etc. Here are a few integrals that may prove useful: ∫sin(kx)dx=−1kcos(kx)+C, ∫cos(kx)dx=1ksin(kx)+C, ∫sin2(kx)dx=x2−14ksin(2kx)+C, and ∫cos2(kx)dx=x2+14ksin(2kx)+

Complete the worksheet. use 3.14 for π and round all decimals to the nearest hundredth.find the volume of the composite three-dimensional figure above. important terms are written in bold.1. the pyramid has a square base that is inscribed in the circular base of the cone. draw an image of the composite shape of the base. 2. if the side length of the square base is 8 units long, what is the diameter of the circular base of the cone from the picture in number 1? 3. now that the diameter has been calculated, what is the circular area of the cone? ignore the square base of the pyramid.? 4. what is the formula for volume of a cone? 5.to calculate the volume of the cone, the height is still needed. if the cone has a lateral surface with a length of 13 units, what is the height of the cone? 6.now find the volume of the cone. do not include the empty space for the pyramid. 7.. the side length of the square base of the pyramid is 8 units long. what is the base area of the pyramid? 8.what is the formula for the volume of a pyramid9. since the cone and the pyramid share the same vertex, what is the volume of the pyramid10.using the volume of the cone and the pyramid, find the volume of the composite shape. remember, the pyramid is empty. 11,. referring to the picture in number 1, what is the area of the composite base knowing that the square is empty? 12what is the formula to find the lateral surface area of a cone? (13find the lateral surface area of the cone14what is the lateral surface area shape of the pyramid? what is the formula for its area? 15to find the lateral surface area of the pyramid the length is still needed. calculate the lateral surface length of the pyramid. 16 now that the lateral surface length is known, what is the lateral surface area of the pyramid17. using the lateral surface areas of the cone and pyramid, along with the area of the composite base, what is the total surface area?