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Write a formula that estimates the change in the volume Vx of a cube when the edge lengths change from a to ax. Then use the formula to estimate the change in volume when x changes from cm to cm.

1 Answer

5 votes

Answer:

a.
dV = 3x^2\ dx

b. See Explanation

Explanation:

Given

Shape: Cube

Solving (a); Formula that estimates the change in edge length

The volume (V) of a cube is:


V = x^3

Where


x = edge\ length

The change in volume is got by:


dV = (d)/(dx)(x^3)

Differentiate
x^3


dV = 3x^2\ dx

Where


dx = x_2 - x_1 i.e. change in x

Solving (b):

The initial and final edge lengths are not given.

In order to solve this question, I'll assume that x changes from 5cm to 5.01cm

So, we have:


x = x_1 = 5cm


x_2 = 5.01cm

Substitute these values in
dV = 3x^2\ dx


dV = 3 * (5cm)^2 * (5.01cm - 5cm)


dV = 3 * (5cm)^2 * 0.01cm


dV = 3 * 25cm^2 * 0.01cm


dV = 075cm^3

User Parth Lotia
by
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