The scale factor between two similar figures is given. The surface area and volume of the smaller figure are given. Find the surface area and volume of the larger figure. scale factor=1:2 SA=90...

The scale factor between two similar figures is given. The surface area and volume of the smaller figure are given. Find the surface area and volume of the larger figure.

scale factor=1:2

SA=90 yd2

V=216 yd3

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embizze | High School Teacher | (Level 1) Educator Emeritus

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It suffices to know that if the scale factor between two similar figures is a:b then (1) all linear correspondences will be in the ratio a:b; (2) the ratio of corresponding areas including the surface area will be `a^2:b^2` ; (3) and the ratio of corresponding volumes will be `a^3:b^3` .

 

The given scale factor is 1:2; the ratio of corresponding areas will be 1:4 and the ratio of corresponding volumes will be 1:8.

 

(a) If the surface area of the smaller figure is 90 square yards, then:

`90/(SA)=1/4` ==>the surface area of the larger figure is 360 square yards.

(b) If the volume of the smaller figure is 216 cubic yards, then the volume of the larger figure can be found by:

`216/V=1/8`  ==> the volume of the larger figure is 1728 cubic yards.

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