Question

The original 24 m edge length x of a cube decreases at the rate of 5 m/min. a. When x = 5 m, at what rate does the cube's surface area change? b. When x = 5 m, at what rate does the cube's volume change? a. When x = 5 m, the surface area is changing at a rate of m^2/min. (Type an integer or a decimal.)

          The original 24 m edge length x of a cube decreases at the rate of 5 m/min.
a. When x = 5 m, at what rate does the cube's surface area change?
b. When x = 5 m, at what rate does the cube's volume change?
a. When x = 5 m, the surface area is changing at a rate of m^2/min.
(Type an integer or a decimal.)

The original 24 m edge length x of a cube decreases at the rate of 5 m/min.
a. When x = 5 m, at what rate does the cube's surface area change?
b. When x = 5 m, at what rate does the cube's volume change?
a. When x = 5 m, the surface area is changing at a rate of m^2/min.
(Type an integer or a decimal.)

Added by Nicole S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Dwijendra Rao

12/21/2021

Step 1

The surface area (A) of a cube is given by A = 6x², where x is the edge length of the cube. The volume (V) of a cube is given by V = x³. Given that the edge length x of the cube is decreasing at a rate of 5 mm/min, or 0.005 m/min, we can denote this as dx/dt = Show more…

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The original 24 m edge length x of a cube decreases at the rate of 5 m/min. a. When x = 5 m, at what rate does the cube's surface area change? b. When x = 5 m, at what rate does the cube's volume change? a. When x = 5 m, the surface area is changing at a rate of m^2/min. (Type an integer or a decimal.)