The 8 foot diameter circular table has a 4 foot wide extension. What is the total area with the extension? How does the area compare to the area of the 10 foot diameter table? Show your work. (3 points)

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sangers1959 sangers1959 · Answer 1 · 2022-07-18T08:51:03+02:00

Answer: the total area with the extension S≈82,3 foot², S>S'.

Step-by-step explanation:

D₁=8 foot D₂=10 foot a wide extension = 4 foot.

1) Let the total area with the extension S is the area of the circular table S₁

plus a wide extension S₂.

Considere S₁:

[tex]R_1=\frac{D_1}{2} \\R_1=\frac{8}{2} \\R_1=4 foot.\\S_1=\pi* R_1^2\\S_1=\pi *4^2\\S_1=16*\pi \\S_1\approx50,3\ foot^2.\\[/tex]

[tex]S_2=8*4\\S_2=32 \ foot^2.[/tex]

[tex]S\approx50,3+32\\S\approx82,3 \ foot^2.[/tex]

2)\ Considere S':

[tex]R_2=\frac{D_2}{2} \\R_2=\frac{10}{2} \\R_2=5 \ foot.\\S'=\pi *R^2\\S'=\pi *5^2\\S'=25*\pi \\S'\approx78,5\ foot^2.[/tex]

S>S'.

Good luck an' have a nice day!