(a) I wanted to determine how much water my sprinkler was using,so I set out a bunch of empty cat food cans at various distancesfrom the sprinkler and noted how high the water was in each canafter one hour. My sprinkler reaches from 0 feet to 16feet away from the sprinkler. The data are given inTable 1. The sprinkler distributes water in a circularpattern, so I assumed that points the same distance from thesprinkler received the same amounts of water.
One way to use the data in Table 1 to estimate how many cubicfeet of water my lawn got from my sprinkler in one hour is to writedown an integral for the volume of water using the method ofshells, and then use a right-endpoint Riemann sum to approximatethis integral. Give your answer in decimal form roundedto the nearest cubic foot.
1 _____ ft3
(b) My neighbor decided to collect the same data for herwatering. Her sprinkler reaches from 0 feet to 21 feetaway from the sprinkler, but she did not set out the cans at evenlyspaced distances and so the calculation is a bit morecomplicated. The data are given in Table 2.
Use the data in Table 2 to estimate how many cubic feet of waterher lawn got from her sprinkler in one hour. Again,write down an integral for the volume of water using the method ofshells, and then use a right-endpoint Riemann sum with subintervalsof different lengths to approximate this integral. Giveyour answer in decimal form rounded to the nearest cubicfoot.
2 _____ft3
I wanted to determine how much water my sprinkler was using, so I set out a bunch of empty cat food cans at various distances from the sprinkler and noted how high the water was in each can after one hour. My sprinkler reaches from 0 feet to 16 feet away from the sprinkler. The data are given in Table 1. The sprinkler distributes water in a circular pattern, so I assumed that points the same distance from the sprinkler received the same amounts of water. One way to use the data in Table 1 to estimate how many cubic feet of water my lawn got from my sprinkler in one hour is to write down an integral for the volume of water using the method of shells, and then use a right-endpoint Riemann sum to approximate this integral. Give your answer in decimal form rounded to the nearest cubic foot. My neighbor decided to collect the same data for her watering. Her sprinkler reaches from 0 feet to 21 feet away from the sprinkler, but she did not set out the cans at evenly spaced distances and so the calculation is a bit more complicated. The data are given in Table 2. Use the data in Table 2 to estimate how many cubic feet of water her lawn got from her sprinkler in one hour. Again, write down an integral for the volume of water using the method of shells, and then use a right-endpoint Riemann sum with subintervals of different lengths to approximate this integral. Give your answer in decimal form rounded to the nearest cubic foot.