A model of a rectangular stove top with four circular burners is shown. The side lengths of the stove top and the diameters of the burners are labeled.
Which measurement is the best estimate of the area in square inches of the stove top that does not include the area of the burners?
A) 108 in.2
B) 492 in.2
C) 420 in.2
D) 528 in.2

C) 420 in^2

Step-by-step explanation:

The stove top has a rectangular shape, so its total area is given by:

where

L = 24 in is the length of the stove top

w = 22 in is the width of the stove top

However, here we have to subtract the area of the 4 circular burners. The area of each circular burner is given by

where r is the radius of each burner. Since the diameter is 6 inches, the radius is half that value, so

r = 3 in

Therefore we can write the net area of the stove top that does not include the area of the burners as

And substituting, we find

So the closest estimate is

C) 420 in^2

step-by-step explanation:

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