Question

read the problem carefully and make sure you answer all the questions. 6. an art classroom has both rectangular and circular tables. the teacher plans to cover each table with a sheet of paper for students to work on. what area of paper should the teacher cut for each rectangular table? what area of paper should the teacher cut for each circular table? round the answer to the nearest tenth, if necessary. there are 12 identical rectangular tables and 6 identical circular tables. what is the total area of paper needed for all of the tables? round the answer to the nearest tenth, if necessary.

Explanation:

Step1: Find area of rectangular table

The rectangular table has length $l = 6$ ft and width $w=2$ ft. The area formula for a rectangle is $A = l\times w$. So, $A_{rect}=6\times2 = 12$ square - feet.

Step2: Find diameter of circular table

The diameter of the circular table $d = 2$ ft 6 in. Convert 6 in to feet: 6 in $=\frac{6}{12}=0.5$ ft, so $d = 2.5$ ft. Then the radius $r=\frac{d}{2}=\frac{2.5}{2}=1.25$ ft.

Step3: Find area of circular table

The area formula for a circle is $A=\pi r^{2}$. Substitute $r = 1.25$ ft, so $A_{circ}=\pi\times(1.25)^{2}=\pi\times1.5625\approx4.9$ square - feet (rounded to the nearest tenth).

Step4: Find total area of rectangular tables

There are 12 rectangular tables. The total area of rectangular tables $A_{total - rect}=12\times A_{rect}=12\times12 = 144$ square - feet.

Step5: Find total area of circular tables

There are 6 circular tables. The total area of circular tables $A_{total - circ}=6\times A_{circ}=6\times4.9 = 29.4$ square - feet.

Step6: Find total area of all tables

$A_{total}=A_{total - rect}+A_{total - circ}=144 + 29.4=173.4$ square - feet.

Answer:

Area of paper for each rectangular table: 12 square feet.
Area of paper for each circular table: 4.9 square feet.
Total area of paper for all tables: 173.4 square feet.