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Vlada [557]
3 years ago
12

Janna has three flat plates, each the same size. She stores them in an L-shaped drawer, as shown so that they fit snuggly inside

, with no spaces between the edges of the drawer and the plates. Approximately how many square centimeters of the bottom of the drawer are not covered by plates?

Mathematics
1 answer:
erica [24]3 years ago
7 0

Answer:  257.143 square centimeter (approx)

Step-by-step explanation:

Here, Three plates are stored in an L-shaped drawer, as shown so that they fit snuggly inside, with no spaces between the edges of the drawer and the plates.

Therefore,

Total area of L- shaped drawer which is not covered by these plates = Total covered area of the L-shaped drawer - Total area of three plates.

Since, the total area of L-shaped drawer= area of square of side 20 cm+ area of rectangle of length 40 and breadth 20.   ( by the given diagram)

Thus,  the total area of L-shaped drawer= 20^2+40\times 20

= 400+800

=1200 square cm

Here, the shape of plates are circular and having the radius of 10 cm. ( by the given diagram)

Therefore area of three circular plates = 3\times \pi\times 10^2

=300\pi square cm

Total area of L- shaped drawer which is not covered by these plates = 1200- 300\pi= 300(4-\pi) =257.142857143≈ 257.143 square cm.

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