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Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides
Question
Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 7 in. long and increasing at the rate of 0.2 in./s. How fast is the volume of the cube changing (in cu in/s) at that instant of time?
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Physics
3 years
2021-09-03T01:36:12+00:00
2021-09-03T01:36:12+00:00 1 Answers
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Answers ( )
Answer:
Therefore the volume of cube is change at the 29.4 cube in./s at that instant time.
Explanation:
Formula
Cube :
The volume of a cube is =![Rendered by QuickLaTeX.com side^3](https://documen.tv/wp-content/ql-cache/quicklatex.com-c6a2527d5aaa746e3dd3e611342f3dc2_l3.png)
The side of length is x in.
Then volume of the cube is (V) =![Rendered by QuickLaTeX.com x^3](https://documen.tv/wp-content/ql-cache/quicklatex.com-a5e0e31e823b4d5c9a90c0d01d5e8fcb_l3.png)
∴ V =![Rendered by QuickLaTeX.com x^3](https://documen.tv/wp-content/ql-cache/quicklatex.com-a5e0e31e823b4d5c9a90c0d01d5e8fcb_l3.png)
Differentiate with respect to t
Given that the side of the cube is increasing at the rate of 0.2 in/s.
i.e
in/s.
And the sides of the cube are 7 in i.e x= 7 in
Putting
and x= 7 in equation (1)
=29.4 cube in./s
Therefore the volume of cube is change at the 29.4 cube in./s at that instant time.