MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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= [tex]20^2+40\times 20[/tex]= 400+800=1200 square cmHere, the shape of plates are circular and having the radius of 10 cm. ( by the given diagram)Therefore area of three circular plates = [tex]3\times \pi\times 10^2[/tex]=[tex]300\pi[/tex] square cmTotal area of L- shaped drawer which is not covered by these plates = [tex]1200- 300\pi= 300(4-\pi)[/tex] =257.142857143≈ 257.143 square cm.