# Frustums can anyone help?

am revising for gcse maths next week does anyone know the following,

the formula for,
1) a cone
2) a frustum

3) how do you rearrange this formula to make h the subject (usually i can do these but have got v strange answer)

s= 2 x pie x d x square root of h squared + d squared

(sorry don't know how to write out any clearer)

4) two mathematically similar frutums have heights of 20cm and 30cm.
the surface area of the smaller frustum is 450cm squared

calculate the surface area of the larger frustum.

Any help would be wonderful,
thanx Olly
HELP HELP HELP HELP

If no one answers i shall hold you all responsible for failing me my Maths GCSE.
Olly
am revising for gcse maths next week does anyone know the following,

the formula for,
1) a cone
2) a frustum

For any pyramid, the volume is:

V=&#8531;bh (where b is the area of the base and h is the height)

A cone is just a special pyramid, so you just find the area of the base:

b=&#960;r² (&#960; is supposed to be pi and r is the radius)

So V=&#8531;&#960;r²h

I'm presuming you mean the frustrum of a cone, which has the formula:
V=&#8531;&#960;h(r²+Rr+R²)
where r and R are the two radii of the top and bottom circles and h is the height and &#960; is pi.
Olly

3) how do you rearrange this formula to make h the subject (usually i can do these but have got v strange answer)

s= 2 x pie x d x square root of h squared + d squared

s=2&#960;d&#8730;(h²+d²)

Divide through by 2&#960;d to get the square root on its own:
s =&#8730;(h²+d²)
2&#960;d
Then square both sides to get rid of the square root:
=h²+d²
4&#960;²d²
Then take away from both sides to leave you with:
-d²=h²
4&#960;²d²
Square root both sides to get h on its own.
Olly
s= 2 x pie x d x square root of h squared + d squared

If you have some sort of graphics program, create a document using freehand pencil to actually draw out the formula, because I can't work it out, if you do that I might be able to help.
Olly
4) two mathematically similar frutums have heights of 20cm and 30cm.
the surface area of the smaller frustum is 450cm squared

calculate the surface area of the larger frustum.

This is a dimensions problem. If you double the length, you quadruple the surface area and increase the volume eightfold because the formula for a length contains x, the formula for an area contains and the formula for a volume contains x³.

You have to times the height of the smaller frustum by 1.5 to get the height of the larger frustum, so you have to times the surface area of the smaller frustum by 1.5² to get the surface area of the larger one:

450x1.5²=450x2.25
=1012.5cm²
Olly
two mathematically similar frutums have heights of 20cm and 30cm.
the surface area of the smaller frustum is 450cm squared

calculate the surface area of the larger frustum.

Let A be any solid. If you expand A by a factor of 2 (ie, make it twice as wide, twice as deep and twice as tall) then the surface area of A increases by a factor of 2^2 = 4.

For your problem, the expansion is by a factor of 1.5 because the height goes from 20cm to 30cm. The surface area hence increases by a factor of 1.5^2 = 2.25.