**Answer:**

**General Formulas and Concepts:**

__Pre-Algebra__

Order of Operations: **BPEMDAS**

- Brackets

- Parenthesis

- Exponents

- Multiplication

- Division

- Addition

- Subtraction

Equality Properties

- Multiplication Property of Equality

- Division Property of Equality

- Addition Property of Equality

- Subtract Property of Equality

__Geometry__

Volume of a Cone:

Diameter: **d = 2r**

__Calculus__

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

**f(x) = cxⁿ**

**f’(x) = c·nxⁿ⁻¹**

**Step-by-step explanation:**

__Step 1: Define__

__Step 2: Rewrite Volume Formula__

*We need to rewrite the cone volume formula in terms of height h only.*

Base *b* = diameter *d* of the circular base

- Define: b = d
- Substitute: b = 2r

We are given that the base of the cone is the same as the height.

- Define: b = 2r
- Substitute: h = 2r

Now solve for height.

- Divide 2 on both sides: h/2 = r
- Rewrite expression: r = h/2

Now find new volume formula.

- Define [VC]:
- Substitute:
- Exponents:
- Multiply:

We now have the same volume formula in terms of height *h* only.

__Step 3: Differentiate__

- Basic Power Rule:
- Simplify:

__Step 4: Solve for height rate__

- Substitute:
- Isolate
*h *rate: - Exponents:
- Multiply:
- Divide:
- Rewrite:

Here this tells us that the rate at which the height is moving at a rate of 0.101859 feet per minute.