A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so that the water level rises at a rate of 4 cm/sec. At what rate is water being poured into the cup when the water level is 3 cm?

32cm³

Step-by-step explanation:

the volume of a cone is

V

=

π

r

2

h

3

in this case, we can relate

h

and

r

as we know that the slope =

h

r

=

10

5

=

2

we can make the volume a formula in a single variable

V

=

π

(

h

2

)

2

h

3

=

π

h

3

12

differentiating wrt time, it follows that

.

V

=

3

π

h

2

.

h

12

=

π

h

2

.

h

4

so to address the question

.

V

=

π

8

2

⋅

2

4

=

32

π

c

m

3

/ sec