Answer: A=276.52 cm²
Step-by-step explanation:
To find the surface area of the figure, we can find the surface area of the rectangular prism and hemisphere. Then we would add them together.
Rectangular Prism
A=2(lw+hl+hw)
Since we are given the length, width, and height, we can directly plug them into the equation and solve.
[tex]A=2((10*5)+(4*10)+(4*5))[/tex]
[tex]A=2(50+40+20)[/tex]
[tex]A=2(110)[/tex]
[tex]A=220 cm^2[/tex]
The surface area for the rectangular prism is 220 cm².
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Hemisphere
A=2πr²
This formula above is derived from the formula for surface area of a sphere.
The surface area of a sphere is A=4πr². Since the picture displays half of a sphere, we divide that by 2. This gives us A=2πr².
Since we have the radius, all we have to do is plug it in.
[tex]A=2\pi (3)^2[/tex]
[tex]A=2\pi (9)[/tex]
[tex]A=18\pi[/tex]
[tex]A=56.52 cm^2[/tex] *Note I used 3.14 instead of π.
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Now that we have the surface area of the hemisphere and rectangular prism, we add them together to find the surface area of the entire prism.
A=220+56.52=276.52 cm²
