Question

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)

Answer 1

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:

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

$S_2=8*4\\S_2=32 \ foot^2.$

$S\approx50,3+32\\S\approx82,3 \ foot^2.$

2)\ Considere S':

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

S>S'.

Good luck an' have a nice day!