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

Reply 1

Olly

HELP HELP HELP HELP

If no one answers i shall hold you all responsible for failing me my Maths GCSE.

Reply 2

meepmeep

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=⅓bh (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=πr² (π is supposed to be pi and r is the radius)

So V=⅓πr²h

I'm presuming you mean the frustrum of a cone, which has the formula:
V=⅓πh(r²+Rr+R²)
where r and R are the two radii of the top and bottom circles and h is the height and π is pi.

Reply 3

meepmeep

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=2πd√(h²+d²)

Divide through by 2πd to get the square root on its own:
s =√(h²+d²)
2πd
Then square both sides to get rid of the square root:
s² =h²+d²
4π²d²
Then take d² away from both sides to leave you with:
s² -d²=h²
4π²d²
Square root both sides to get h on its own.

Reply 4

Fleffzilla

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.

Reply 5

meepmeep

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 x² 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

Reply 6

Jonny W

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.