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area of the rectangle

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1. A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x.


2. The diameter of a spherical balloon is 8 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the balloon as a function of x.
Note the volume of a sphere with radius R is V=4/3(pi)R^3

The increase in volume is equal to _____________ cm^3

3. A rectangle has its base lying on the x axis and its upper corners on the parabola y=38â?'x^2. If the upper right corner is (s,t), express the area A of the rectangle as a function of s.

The area of the rectangle is A=________

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The area of the rectangle is examined.

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1) Let a be the height of the box. Then, since its base is a square with side x, the volume of the box is a*x*x = ax^2. And we know, it's 7.
So, ax^2 = 7, which means a = 7/(x^2)

Now, the surface of the box consists of:
the base, which is a square of side x,
the top, which is again a square of side x,
and 4 sides, each of which is a rectangle ...

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