Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 24 feet high

0.0221 feet per minute.

Step-by-step explanation:

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

Rate of Change of the Volume,

Since gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. Therefore, the Volume of the cone is increasing at a rate of 10 cubic feet per minute.

We want to determine how fast is the height of the pile is increasing when the pile is 24 feet high.

We have:

When the pile is 24 feet high, the height of the pile is increasing at a rate of 0.0221 feet per minute.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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step-by-step explanation: