# A box with a square base has a surface area including the top of 3 m^2.

• Feb 5th 2009, 03:56 PM
Jasmina8
A box with a square base has a surface area including the top of 3 m^2.
1. A box with a square base has a surface area including the top of 3 m^2. Express the volume V of the box as a function of the width w of the base.

2. A stone is thrown into a lake and t seconds later after the splash the diameter of the circle of the ripples is t meters.
a. Express the circumference C of this circle as a function of t.
b. Express the area A of this circle as a function of t.

• Feb 5th 2009, 04:17 PM
skeeter
Quote:

Originally Posted by Jasmina8
1. A box with a square base has a surface area including the top of 3 m^2. Express the volume V of the box as a function of the width w of the base.

surface area ... $\displaystyle 2w^2 + 4wh = 3$

use the surface are equation to solve for h in terms of w, then substitute for h in the volume equation ...

$\displaystyle V = w^2h$

Quote:

2. A stone is thrown into a lake and t seconds later after the splash the diameter of the circle of the ripples is t meters.
a. Express the circumference C of this circle as a function of t.
b. Express the area A of this circle as a function of t.
you are given that $\displaystyle d = t$ ...

a. hint ... $\displaystyle C = \pi d$

b. two hints ... $\displaystyle A = \pi r^2$ and $\displaystyle r = \frac{d}{2}$