Question

Sara has a stack of 8 plates, each plate is 0.5 inches tall and she is trying to wrap them as a gift.

The largest plate has a diameter of 10 inches and each plate has a diameter of 1 inch smaller
than the previous plate. She has a cylindrical box with a radius of 5 in that can hold 150 cubic inches.
Will her plates fit in the box?
Plz help!!

Answer 1

The plates will not fit into the box.

Explanation:

Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of
`0.5in*8 = 4inches`.

Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.

What we want to figure out now is the height of the cylindrical box to see if it is greater than or equal to 4 inches—the height of the stack of plates.

The volume of a cylinder is
`\pi R^2h`, and since for our cylindrical box the volume is 150 cubic inches; therefore,

`\pi R^2h = 150in^3`

putting in
`R = 5in` and solving for height
`h` we get

`h = (150in^3)/(\pi (5)^2)`

`h = 1.91\: inches`,

which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.