Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Surface area of a frustum?

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

The surface area of the smaller frustum is 450 cm squared

Calculate the surface area of the larger frustum.

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• Philip
Lv 6
1 month ago

1st  degree ratio of larger/smaller = (3/2).;

2nd degree ratio of larger/smaller = (3/2)^2 = (9/4).;

Surface area (smaller frustrum) = 450cm^2.;

Surface area (..larger frustrum) = (9/4)(450)cm^2 = 2.25(450)cm^2 = (900+112.5)cm^2 =;

1012.5 cm^2.

• 1 month ago

The surface area of the larger frustum is 1012.5 cm^2.

• cosmo
Lv 7
1 month ago

The big one is 1.5 times the smaller one in linear size.

The surface area scales as the square of the linear size, therefore

surface area of big one = 1.5^2 x 450 cm^2 = 1012.5 cm^2

• 1 month ago

The linear (1D) measurements (heights) of the large to the small are in the ratio 30/20 = 3/2.

That means all linear (1D) measurements are 3/2 (or 1.5) times as much for the larger shape.

Since they are similar shapes, the area (2D) measurements (surface area) of the large to the small will be in the ratio of (3/2)² = 9/4.

That means all area (2D) measurements are 9/4 (or 2.25) times as much for the larger shape.

9/4 * 450 cm²

= 1,012.5 cm²

Note: the pattern continues for volumes (3D) where the volume of the larger solid would be (3/2)³ = 27/8 = 3.375 times the volume of the smaller.