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

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To calculate the surface area of the larger frustum, recognize that the frustums are mathematically similar, meaning their dimensions scale proportionally. The height ratio is 30cm to 20cm, or 3/2, which implies that the area ratio will be the square of this ratio, resulting in 9/4. Given the smaller frustum's surface area is 450cm², the larger frustum's surface area can be found by multiplying 450 by 9/4, yielding 1012.5cm². The discussion highlights confusion around applying dimensional adjustments and the surface area formula, but the key takeaway is understanding the relationship between similar shapes and their areas. This approach simplifies the calculation process for similar geometric figures.
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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
 
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Trail_Builder said:
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
 
would it be 9/4?
 

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