Aconical 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 2 cm/sec. at what rate is water being poured into the cup when the water level is 8 cm?

At the rate of   water being poured into the cup when the water level is cm

The above figure shows the variables

Radius of conical cup() cm

Height of the conical cup () cm

Height of water level in cup at time , cm

Radius of water at time cm

Volume of water at time

Triangle is similar to triangle

find which is rate of water being poured in cup.

The volume of a cone is,

Differentiate with respect to we get:

Therefore ,

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Water is being pored in the cone with the rate of 401.92 cm³ per second.

Step-by-step explanation:

There is a cone having height h = 10 cm and radius r = 10 cm

That means h = r

Rate of change of water level cm per second

Since volume of a cone is represented by the formula,

Now we have to find the value of .

Since r = h

For h = 8 cm and cm per second.

= 401.92 cubic cm per second

Therefore, water is being pored with the rate of 401.92 cm³ per sec.

took the test it's 94

b

step-by-step explanation:

the word superfluous means unnecessary