- E An Architect Designs A Shade Structure That Will Be Built On Flat Ground The Shape Of The Structure Is As Follows 1 (133.7 KiB) Viewed 171 times
- E An Architect Designs A Shade Structure That Will Be Built On Flat Ground The Shape Of The Structure Is As Follows 2 (224 KiB) Viewed 171 times
- E An Architect Designs A Shade Structure That Will Be Built On Flat Ground The Shape Of The Structure Is As Follows 3 (143.06 KiB) Viewed 171 times
The floor of the structure is in the form of a truncated isosceles triangle. The base of the triangle, along the east end of the building, is 40m long. The western edge of the floor is 20m long. The length of the floor along its midline from west to east is also 20m. A plan of the floor area is shown y Floor area looking from above 20 10 below. 0 10 20 X -10 -20 The edge of the roof is directly above the edge of the floor. The architect would like to find the volume between the roof of the structure and its floor. (i) The interval [0, 20] is divided into n equal subintervals width Ax. Draw an incremental volume element, width Ax, that can be used to find the volume between the roof of the structure and its floor. On your sketch indicate the height, width and depth of the volume element. These may be expressed in terms of x.
(ii) Use sigma notation to write down the Riemann sum Sn that approximates the volume between the roof and the floor with the volume elements like the one you have drawn in part (i). You may assume that the kth subinterval contains an element which can be used to write down the Riemann sum. (iii) Write down the integral that is given by lim Sn and which n→∞ corresponds to the volume between the roof of the structure and its floor. Evaluate this integral and find an exact expression for the volume. (Do not use your calculator to evaluate this. Leave it in terms of e.)