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.

S=_______

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=38รข?'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=________

Solution Preview

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 ...

... 1.Different pets need to have different areas. ... 2.Define the shape of the rectangular area by establishing a ... between the length and width of the rectangle. ...

Maximizing the area of a rectangle. ... y= height of the inscribed rectangle. Now we wish to MAXIMIZE the total AREA of the rectangle. A = (length of base) (height). ...

Quadratic Equation Application Word Problem : Maximizing Rectangular Area. ... 3. From 2, we know that the maximum area of the rectangle is reached when x = 50 . ...

... Draw the rectangle and find the total of the areas of the ... 3. Suppose that the area of the x+2 by x+4 rectangle drawn in the last exercise is actually 120 ...

Intermediate Algebra : Solving Equations and Inequalities and Maximum Area of a Rectangle Given Perimeter. Solve the equation by the method of your choice. ...