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please help. answer is 62.1m(squared) and the objects are composite! please show the work, no matter what i do i cant seem to get the right answer.

please help. answer is 62.1m(squared) and the objects are composite! please show the-example-1

1 Answer

5 votes

Answer:


SA=62.1\ m^2

Explanation:

step 1

Find the surface area of the smaller rectangular prism


SA=2B+Ph

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism


SA=2[(2.5)(1.5)]+2(2.5+1.5)(1.5)


SA=7.5+12=19.5\ m^2

step 2

Find the surface area of the cube


SA=6s^2

where

s is the length side of the cube


SA=6(2.5^2)=37.5\ m^2

step 3

Find the lateral area of the cylinder


LA=\pi DL

where

D is the diameter of the base

L is the length of cylinder


LA=(3.14)(0.5)(3.5)=5.495\ m^2

step 4

Find the area of the base of cylinder


A=\pi r^(2)

we have


r=0.5/2=0.25\ m ----> the radius is half the diameter


A=(3.14)(0.25)^(2)=0.19625\ m^2

step 5

Find the surface are of the composite figure

we know that

The surface area of the composite figure is equal to the surface area of the smaller rectangular prism plus the lateral area of the cylinder, plus the surface area of the cube, minus the area of the two bases of cylinder

so


SA=19.5+5.495+37.5-2(0.19625)=62.1\ m^2

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