A block of ice has a square top and bottom and rectangular sides. At a certain point in time, the square top and bottom each have a length of 30 cm, which are decreasing at a
rate of 2 cm/h. At the same time, the height of the ice block is 20 cm and decreasing at
3 cm/h. How fast is the ice melting?

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Geometry

Volume of a Rectangular Prism: V = lwh

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: Differentiate

Rewrite [VRP]:                                                                                                 Differentiate [Basic Power Rule]:                                                                        

Step 3: Solve for Rate

Substitute:                                                                                                           Multiply:                                                                                                              

Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.

Ibelieve it would be letter c (: