All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the volume changing when each edge is 2 centimeter(s)?
(b) How fast is the volume changing when each edge is 14 centimeter(s)?

The volume will be:

(a) 24 cm³

(b) 1176 cm³

Given:

Expanding rate,

Let,

(a)

When,

then,

→

Let,

→

→

(b)

When,

then,

→

Let,

→

→

Thus the above answer is correct.

Learn more about cube here:

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Step-by-step explanation:

As all edges of a cube are expanding at a rate of 2 centimeters per second.

i.e ds/dt = 2 cm/s

The formula of volume of cube: V = s³

Differentiating the volume:

dv/dt = 3s²

Write ds/dt following derivative of volume

dv/dt = 3s² ds/dt

plug in the value: ds/dt = 2 cm/s

dv/dt = (3s²) (2)

dv/dt = 6s²

Given the edge is 2cm.

so plug in the value: s=2

dv/dt = 6s²

          = 6(2)²=6(4)=24 cm³/per second

SIMILARLY,

When the edge is 14cm

dv/dt = 6s²

plug in the value: s=14

dv/dt = 6s²

         = 6(14)²=6(196)=1176 cm³/per second

Thus,

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: