# Algebra 2 and Geometry word problems

• Mar 29th 2008, 09:32 AM
wisezeta
Algebra 2 and Geometry word problems
Step by step solution would be nice (Nod)

a) two cones have the same volume. one of them has a radius of 3 cm less than the other and a height twice that of the first. what are the radii of the two cones?

b) a frame of uniform width surrounds a 16 cm by 20 cm picture so that the total area fo the framed picture is 464 cm^2. what is the width of the frame?

c)the denominator of a fraction is an integer that is one greater than the numerator.a second fraction is the reciprocal of the integer that is one less than the numerator of the first fraction. if the product of the two fractions is 3/8, identify the first fraction.

d)an isosceles triangle has a perimeter of 50 cm. the sum of the length of the base and the height of the triangle is 31 cm. find the area of the triangle.
• Mar 29th 2008, 09:39 AM
polakio92
glad to see someone has the same problems as me, and needs help on the same problems as me.
• Mar 29th 2008, 10:07 AM
wingless
Quote:

Originally Posted by wisezeta
a) two cones have the same volume. one of them has a radius of 3 cm less than the other and a height twice that of the first. what are the radii of the two cones?

Volume of a cone:
$\frac{\pi.r^2.h}{3}$

As two cones have the same volume,

$\underbrace{\frac{\pi.r^2.h}{3}}_{\text{Cone I}} = \underbrace{\frac{\pi.r^2.h}{3}}_{\text{Cone II}}$

Cone II's radius is 3 cm less and its height is twice of Cone I.

Then if Cone I's radius is r, Cone II's is r-3. Likely, if Cone I's height is h, Cone II's height is 2h.

$\underbrace{\frac{\pi.r^2.h}{3}}_{\text{Cone I}} = \underbrace{\frac{\pi.(r-3)^2.2h}{3}}_{\text{Cone II}}$

Solve this and r will be the radius of Cone I, as we set it.

Quote:

Originally Posted by wisezeta
c)the denominator of a fraction is an integer that is one greater than the numerator.a second fraction is the reciprocal of the integer that is one less than the numerator of the first fraction. if the product of the two fractions is 3/8, identify the first fraction.

Let A = fraction 1 and B = fraction 2.

A = $\frac{n}{n+1}$

B = $\frac{1}{n-1}$

And we know that $\frac{n}{n+1}\cdot \frac{1}{n-1} = \frac{3}{8}$

Solve it.
• Mar 29th 2008, 10:09 AM
wisezeta
Omg thank u so much
• Mar 29th 2008, 12:36 PM
CHS_math
Quote:

Originally Posted by wisezeta
Omg thank u so much

This is Mr. Kolev. I expect to see all of this help documented in your portfolio.