Answer :
Answer:
66 candies can be fitted in the pyramid shaped box.
Step-by-step explanation:
If length, width and height of the rectangular box es are l, w, and h respectively.
Then volume of the rectangular box (V) = (Length × width × height)
V = lwh
Now we have to find the volume of a pyramid having length, width and height same as the rectangular box,
Then volume of the pyramid V' = [tex]\frac{1}{3}(\text{Area of the rectangular base})(\text{Height})[/tex]
V' = [tex]\frac{1}{3}(l\times w)(h)[/tex]
Ratio of volumes = [tex]\frac{\frac{1}{3}lwh}{lwh}[/tex] = [tex]\frac{1}{3}[/tex]
If the number of candies in the pyramid of is x then the ratio of candies in pyramid shaped box and rectangular box = [tex]\frac{x}{200}[/tex]
Now the ratio of volumes of the boxes will be equal to the ratio of number of candies in the boxes.
[tex]\frac{x}{200}=\frac{1}{3}[/tex]
x = [tex]\frac{200}{3}[/tex]
x = 66.67
x ≈ 66 candies
Therefore, 66 candies can be fitted in the pyramid shaped box.