Aconical tank is 10 feet across and 12 feet deep if water is flowing into the tank at a rate of 10 cubic feet per minute find the rate of change of the depth of the water when the water is 8 feet deep

0.286 ft per minute ( approx )

Step-by-step explanation:

Let r represents the radius and h represents the height of the cone,

If the conical tank is 10 feet across and 12 ft deep,

Diameter = 10 ft, h = 10 ft

⇒ 2r = 10 ⇒ r = 5 feet,

Now, radius of a cone and its height is always in same proportion,

Now, volume of a cone,

From equation (1),

Differentiating with respect to t ( time ),

Here,

Hence, the rate of change of the depth of the water would be 0.286 ft per minute

78.59 is the mean

step-by-step explanation: