A sand storage tank used by the highway department for winter storms is leaking. As the sand leaks out, it forms a conical pile. The radius of the base of the pile increases at a rate of 0.75 inches per minute. The height of the pile is always twice the radius of the base. How fast is the volume of the pile increasing at the instant that the radius of the base is 6 inches?

Volume of the pile is increasing at the rate =

Step-by-step explanation:

Given:

The height of the pile is always twice the radius of the base.

Radius of the conical pile r = 6 inches.

When r = 6

The increasing rate of the radius of pile

We need to find the volume of the pile when the radius of the base is 6 inches.

Solution:

We know the volume of the cone.

Where:

r = radius of the cone

h = Height of the cone

Substitute h = 2r in the above formula because the height of the pile is always twice the radius of the base.

Now, differentiate both side of the equation with respect to t.

Substitute r = 6 and .

Therefore, volume of the pile is increasing at in a 6 inches radius of the base.

step-by-step explanation:

the first 5 right here the next 5 i will upload as separate question

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13