Respuesta :
Answer:
therefore the left over board is 0.216[tex]a^{2}[/tex] where 'a' is length of a side of the black poster board.
Step-by-step explanation:
i) Sasha cuts 4 identical circles from a square piece of black poster.
ii) let each side of the square piece be a.
iii) let us divide the square piece into four equal square parts from which the four identical circles will be cut
iv) therefore the side of each smaller square will be [tex]\frac{a}{2}[/tex].
v) therefore the diameter of each identical circle will be [tex]\frac{a}{2}[/tex]
vi) therefore the radius if each of the four identical circles will be [tex]\frac{1}{2} \times \frac{a}{2} = \frac{a}{4}[/tex]
vii) the area of each of the four identical circles will be = [tex]\pi \times (\frac{a}{4} )^{2} = 3.14 \times (\frac{a}{4}) ^{2} = \frac{3.14a^{2}}{16} = 0.196a^{2}[/tex]
vii) the area of each of the four smaller squares = [tex]\frac{a}{2} \times \frac{a}{2} = \frac{a^{2} }{4} = 0.25a^{2}[/tex]
viii) therefore the area left over from each of the four smaller squares
= 0.25[tex]a^{2}[/tex] - [tex]0.196a^{2}[/tex] = 0.054[tex]a^{2}[/tex]
ix) therefore the left over board is given by 4 [tex]\times[/tex] 0.054[tex]a^{2}[/tex] = 0.216[tex]a^{2}[/tex] where a is length of a side of the black poster board.
