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Find the surface area and volume of the large solid.

Find the surface area and volume of the large solid.-example-1
User PixelPlex
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1 Answer

23 votes
23 votes

Part 1

Find out the surface area of the larger solid

Remember that

If two figures are similar, then, the ratio of their surface areas is equal to the scale factor squared

In this problem

scale factor=1/2

so

Let

A ----> surface area of the smaller solid

B ----> surface area of the larger solid

we have that

(A/B)=[scale factor]^2

A=208 in2

substitute

208/B=(1/2)^2

208/B=1/4

B=208*4

B=832 in2

therefore

The surface area of the larger solid is 832 square inches

Part 2

Find out the volume of the larger solid

Remember that

If two figures are similar, then, the ratio of their volumes, is equal to the scale factor elevated to the cubic

so

Let

C ----> volume of the smaller solid

D ----> volume of the larger solid

we have that

C/D=[scale factor]^3

C=192 in3

substitute

192/D=(1/2)^3

192/D=1/8

D=192*8

D=1,536 in3

therefore

The volume of the larger solid is 1,536 cubic inches

User Amjad
by
2.8k points