Question

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.

Answer 1

`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`