Calculating Surface Area of Mathematically Similar Frustums: A Beginner's Guide

[Trail_Builder]

hi, soz, this is way below my level but i havnt done these in age and are tired and getting in a muddle. thnx for clarifying things...

Homework Statement

Two mathematically similar frustums have heights of 20cm and 30cm

The surface area of the smaller frustum is 450cm^2

qu) calculate the surface area of the larger frustum

Homework Equations

surface area of a frustum = 2pi x dia. x (square root)[h^2 + d^2]

The Attempt at a Solution

right, i am being a moron i know, but i forget where the dimensional adjustment to

20/450 = 30/ans

is amplied. I was thinking of something like:

20/450^2 = 30/ans^2

but then i tried using my own example of stuff like cubes and swaures and stuff and it didnt work.

then i tried

20^2/450 = 30^2/ans

but then using my own dimensional examples it didnt work.

i also tried using the surface area formula for frustums, but that didnt work either.


i know i am being a dumbhead, but hey, i guess its got i havn't answered these qus in years lol. and it called a frustum for a reason ;)


thnx

 

[HallsofIvy]

hi, soz, this is way below my level but i havnt done these in age and are tired and getting in a muddle. thnx for clarifying things...

Homework Statement

Two mathematically similar frustums have heights of 20cm and 30cm

The surface area of the smaller frustum is 450cm^2

qu) calculate the surface area of the larger frustum

Homework Equations

surface area of a frustum = 2pi x dia. x (square root)[h^2 + d^2]

Irrelevant! You are told that these figures are "mathematically similar" which means that they have the same "shap": all lengths in the large one are 30/20= 3/2 the corresponding small one. Since the "area" of anything depends upon multiplying two lengths together, area always is proportion to the square of a length. If in going from the smaller to the larger, all lengths are multiplied by 3/2, what is the area multiplied by?

The Attempt at a Solution

right, i am being a moron i know, but i forget where the dimensional adjustment to

20/450 = 30/ans

is amplied. I was thinking of something like:

20/450^2 = 30/ans^2

but then i tried using my own example of stuff like cubes and swaures and stuff and it didnt work.

then i tried

20^2/450 = 30^2/ans

but then using my own dimensional examples it didnt work.

i also tried using the surface area formula for frustums, but that didnt work either.


i know i am being a dumbhead, but hey, i guess its got i havn't answered these qus in years lol. and it called a frustum for a reason ;)


thnx

 

[Trail_Builder]

would it be 9/4?