Answer:
[tex]SA=62.1\ m^2[/tex]
Step-by-step explanation:
step 1
Find the surface area of the smaller rectangular prism
[tex]SA=2B+Ph[/tex]
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
[tex]SA=2[(2.5)(1.5)]+2(2.5+1.5)(1.5)[/tex]
[tex]SA=7.5+12=19.5\ m^2[/tex]
step 2
Find the surface area of the cube
[tex]SA=6s^2[/tex]
where
s is the length side of the cube
[tex]SA=6(2.5^2)=37.5\ m^2[/tex]
step 3
Find the lateral area of the cylinder
[tex]LA=\pi DL[/tex]
where
D is the diameter of the base
L is the length of cylinder
[tex]LA=(3.14)(0.5)(3.5)=5.495\ m^2[/tex]
step 4
Find the area of the base of cylinder
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=0.5/2=0.25\ m[/tex] ----> the radius is half the diameter
[tex]A=(3.14)(0.25)^{2}=0.19625\ m^2[/tex]
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
[tex]SA=19.5+5.495+37.5-2(0.19625)=62.1\ m^2[/tex]
