Question

A candy comapny can fit 200 piecies of candy into a standers rectangular box for a special promotion the company designs a pyramid with the smae dimensins for the base and height assuming the candy can change its shape to fit the box how many pieces of candy could fit into the new pyramid sheped box?

Answer 1

66 candies can be fitted in the pyramid shaped box.

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' =
`(1)/(3)(\text{Area of the rectangular base})(\text{Height})`

V' =
`(1)/(3)(l* w)(h)`

Ratio of volumes =
`((1)/(3)lwh)/(lwh)` =
`(1)/(3)`

If the number of candies in the pyramid of is x then the ratio of candies in pyramid shaped box and rectangular box =
`(x)/(200)`

Now the ratio of volumes of the boxes will be equal to the ratio of number of candies in the boxes.

`(x)/(200)=(1)/(3)`

x =
`(200)/(3)`

x = 66.67

x ≈ 66 candies

Therefore, 66 candies can be fitted in the pyramid shaped box.