# Thread: 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.

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.

2. 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 ... $2w^2 + 4wh = 3$

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

$V = w^2h$

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 $d = t$ ...

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

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