Question

A square piece of material with sides 150cm is used to make a circular table cloth. The diameter of the completed cloth must be 1.2m and 5cm is provided for a hem. How much material is wasted?

Answer 1

Answer:

$\textbf{Area of the material wasted=10223.21 \:cm^2 }$

Step-by-step explanation:

Let a and r be the length of the side of the square piece of material and radius of the circular table

$\text{Given:}$

$\text{Length of the side of the square piece of materal, a = 150 cm}$

$\text{Diameter of the circular table =125 cm}$

$\text{2r =125 cm}$

$\implies\text{r =62.5 cm}$

$\text{Area of the material wasted= Area of the square piece of material - Area of the circular table}$

$\text{Area of the material wasted= a^2-\pi\:r^2 }$

$\text{Area of the material wasted= (150)^2-\frac{22}{7}\:(62.5)^2 }$

$\text{Area of the material wasted= 22500-\frac{22}{7}(62.5\times62.5) }$

$\text{Area of the material wasted=22500-12276.79}$

$\therefore\boxed{\textbf{Area of the material wasted=10223.21 \:cm^2 }}$