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.
- PhilipLv 6hace 1 mes
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 =;
- KrishnamurthyLv 7hace 1 mes
The surface area of the larger frustum is 1012.5 cm^2.
- cosmoLv 7hace 1 mes
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
- PuzzlingLv 7hace 1 mes
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.