Answer to Question #92199 in Geometry for Masungulo

Question

A square piece of material with sides 150 cm is used to make a circular table cloth. The diameter of
the completed cloth must be 1,2 m and 5 cm is provided for a hem. How much material is wasted?
(Answer correct to 2 decimal places.)
1. 1,30 m2
2. 92,26 cm2
3. 0,92 m2
4. 129,97 cm2

Answer 1

First, we must calculate the area of the starting material, which has square shape:

S(start) = a^2 = (1.50 m)^2 = 2.25 m^2

Further we have to calculate the area of the circular cloth. Here we must add 0.05 m on each side to provide enough material for the hem:

S(cloth) = 1/4*pi*(diameter + 2*hem)^2 = 1/4*3.14*(1.2 m + 2*0.05 m)^2 = 1.33 m^2

Now, the residue material area can be calculated as a difference between S(start) and S(cloth):

S(res.) = 2.25 m^2 - 1.33 m^2 = 0.92 m^2

Thus, the correct answer is 0.92 m^2 or option 3.