1. ## work:

A tank in the form of an inverted right circular cone is 8m across the top and 10m deep. If the tank is filled to a height of 9m with water, find the work done in pumping the water to the top of the tank:

the radius is 4, the depth is 10
so
the coordinates of the line passes through
(4,0) and (0,-10)
Equation of the line is: (y-(-10)) = 5/2(x - 0)
x = 2/5y + 4

work is :

$d(W) = 9180\pi(\frac{2}{5}y + 4)^2ydy$
and multiplied by y is the change in length to the top of the cone right?

is the math model correct?
$9180\pi \int_{-9}^{-1} (\frac{2}{5}y + 4)^2 ydy$

thank you so much

2. A tank in the form of an inverted right circular cone is 8m across the top and 10m deep. If the tank is filled to a height of 9m with water, find the work done in pumping the water to the top of the tank:

the radius is 4, the depth is 10
so
the coordinates of the line passes through <---This should be "the line passes through the coordinates"
(4,0) and (0,-10)
Equation of the line is: (y-(-10)) = 5/2(x - 0)
x = 2/5y + 4

work is :

d(W) = 9180pi[(2/5)y + 4)^2ydy
and multiplied by y is the change in length to the top of the cone right?

I assume your 9180 is the density of water in metric,
9180 newton/cu.m.
Should that not be 9800 newton/cu.m. ?
Or, using your numbers, 9810 N/cu.m.?

"the coordinates of the line passes ..."
That should be "the line passes through the coordinates"

"(4,0) and (0,-10)"
That means your (0,0) is the center of the circular top of the cone.

"and multiplied by y is the change in length to the top of the cone right?"
Should be:
"and it is multiplied by (-y) because (-y) is the change in height to the top....."

---------------------------------------------

is the math model correct?
$9180\pi \int_{-9}^{-1} (\frac{2}{5}y + 4)^2 ydy$

The y in the "y dy" should be negative. Because all y's below the (0,0) are negative.

The boundaries for integration should be from y = -10 to y = -1.