A marble is 12 mm in diameter. what is the smallest height of a box that is 96 mm square that can hold 200 marlbles and still have a lid fit on the box without interference?
A.12mm B.24 C.36mm D.48mm E.60mm
By sheer coincidence this same question was posted on March3 , three years ago
http://www.jiskha.com/display.cgi?id=1299163469
D
To find the smallest height of the box that can hold 200 marbles, we need to calculate the volume of the box and divide it by the number of marbles it can hold.
The volume of a box can be determined by multiplying its length, width, and height. In this case, the box has a square base, so the length and width are both 96 mm.
Let's assume the height of the box is 'h' mm. The volume of the box is then:
Volume of the box = length * width * height
Volume = 96 mm * 96 mm * h mm
To hold 200 marbles, the box's volume needs to accommodate the volume of all the marbles.
The volume of a marble can be calculated using the formula for the volume of a sphere:
Volume of a sphere = (4/3) * π * r^3
Given that the diameter of the marble is 12 mm, the radius (r) is half of that, which is 6 mm.
Volume of one marble = (4/3) * π * (6 mm)^3
To find the smallest height of the box, we divide the total volume of the box by the volume of one marble (multiplied by 200 to hold 200 marbles).
Volume of the box / Volume of one marble * 200 = h
(96 mm * 96 mm * h mm) / [(4/3) * π * (6 mm)^3] * 200 = h
Now we can solve this equation to find the smallest height of the box.