Question

All edges of a cube are expanding at a rate of 7 centimeters per second. (a) How fast is the surface area changing when each edge is 3 centimeters? cm^2/s (b) How fast is the surface area changing when each edge is 12 centimeters? cm^2/s

A) (63cm^2/s, 252cm^2 /s
B) (147cm^2 /s, (b) 588cm^2/s
C) Both a and b
D) 126cm ^2 /s, (b)504cm^2 /s

Answer 1

The rate at which the surface area of the cube is changing can be found using the formula SA' = 6s^2 * s', where s is the length of each edge of the cube and s' is the rate at which s is changing. When each edge is 3 centimeters, the rate of change of surface area is 126 cm^2/s, and when each edge is 12 centimeters, the rate of change of surface area is 504 cm^2/s.

To find the rate at which the surface area of the cube is changing, we can use the formula:

SA' = 6s^2 * s'

Where SA' is the rate of change of surface area, s is the length of each edge of the cube, and s' is the rate at which s is changing.

(a) When each edge is 3 centimeters, s' = 7 cm/s, so:

SA' = 6(3^2)(7) = 126 cm^2/s

(b) When each edge is 12 centimeters, s' = 7 cm/s, so:

SA' = 6(12^2)(7) = 504 cm^2/s