Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the water level when the water is 6 m deep. (1 L = 1000cm^3)

For this case we know that represent the radius, the height and the rate given is:

And replacing we got:

And that represent

Step-by-step explanation:

For a tank similar to a cylinder the volume is given by:

For this case we know that represent the radius, the height and the rate given is:

For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:

And solving for we got:

We need to convert the rate given into m^3/min and we got:

And replacing we got:

And that represent

i’m here for points.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.