Find the lateral (side) surface area of the cone generated by revolving the line segment y equals nine sevenths x , 0 less than or equals x less than or equals 7, about the x-axis. Check your answer with the following geometry formula. Lateral surface areaequalsone half times base circumference times slant height

lateral surface area  =118.42

Step-by-step explanation:

y= 9x/7

dx/dy =

Given x range as  from 0 ≤ x ≤ 7 ⇒ The range of x is

a= 9x/7 = 9(0)/4 = 0

b = 9x/7= 9(7)/4 = 9

lateral surface area of the cone

=

=118.42

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

step-by-step explanation:

the answer is 128