## word problem

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Luke53
Posts: 54
Joined: Sun Mar 13, 2011 9:46 am
Contact:

### word problem

The volumes and total surface area's of a right-angled cone and a cilinder are the same and so are their heights. Find the radius of their ground planes.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Luke53
Posts: 54
Joined: Sun Mar 13, 2011 9:46 am
Contact:

### Re: word problem

Formula's for the volumes:
cone: v = (pi * x^2 * h) / 3
cilinder: v = pi * y^2 * h
where x = radius of the cone and y = radius of the cilinder, and since h is te same for both (given).
x^2 = 3 * y^2 so x = sqrt(3) * y (1)
Formula's of the surfaces:
S cone = pi * x * sqrt(x^2 + h^2) + pi * x^2 (2)
S cilinder = (2 * p i * y * h) + (2 * pi * y^2) (3)
Subst. (1) into (2) and (3) and setting (2) and (3) equal to each other, don't give the same results when worked out.
So, I think the statement of this word problem is false.
Luke.

anonmeans
Posts: 84
Joined: Sat Jan 24, 2009 7:18 pm
Contact:

### Re: word problem

Are you maybe only supposed to use the "lateral" surface areas, so you don't include the areas of the bases?