4. The base of a greenhouse is a circle with radius 3 metres. There is a central irrigation sprinkler in the roof, which waters the greenhouse unevenly. The rate of irrigation 7* metres from the centre of the 'r + 2 greenhouse (measured along the ground) is litres of water per square metre per day. T+1 Figure 5: Irrigation rate across greenhouse: light colours are higher, dark are lower (a) Let m and Am be positive constants, with O 5 7'0 S 713+ Am 3 3. Interpret, in terms of our model, T0+2 T0+1 27T7'0 ATO - when A'ro is small. (Remember to include units, as always.) (b) Interpret, in terms of our model, the value you computed in 3(b). ((3) Interpret, in terms of our model, the value you computed in 3(e). 5. Explain why it was convenient to use approximate values for the volumes of the thin cylinders, rather than the exact values, in this assignment. :c2 :131 3. Let S be the solid formed by rotating the nite area bounded by a? : 0, a: : 3, y : 0, and y : around the yaxis. In this question, we'll nd the volume of 5' using cylindrical shellsl. 19' Figure 3: the region rotated to form 3 (a) Sketch the portion of the solid resulting from rotating the nite area bounded by a: = 1, m = 1.1, I 2 $771 y = U, and y 2 around the y-axis. (b) Use your formula from 2(e) to approximate the volume of the solid in (a). (c) What is the approximate volume of a cylindrical shell with radius :50, width A330, and height (.50 -- 2 ? (Continue to use the formula from 2(e).) $0 -- 1 (d) We can imagine the solid 3 consisting of layers of thin cylinders, or cylindrical shells, similar to the shape you found in (a). Figure 4: approximating S using cylinders We want to create a collection of these cylindrical shells that makes up all of S. What are the largest and smallest radii such shells could have? (e) \"Adding up" the volumes of all the cylindrical shells will give us the volume of 5'. Find the volume of S by evaluating l: f 9(53) d2: where a and b are the limits found in (d), and 9(23) die is adapted from (c) 1This method is used in Example 1.6.9 of the CLP-2 textbook