Question

Micaela has a bat that is 30 inches long. She wants to fit it in a cube shaped box that has sides that are 17 inches. Will the bat fit? Justify your answer.

Answer 1

No because 30 divided by 17 = 1.765

Answer 2

The sides of the cube are 17 inches each

It means the length = 17 inches , width = 17 inches , and height = 17 inches

Now One thing we can say just by seeing at the length of the bat , that it cannot fit straight lying on sides ,

But , it can fit diagonally in the cube box.

So what we have to do is to find the diagonal length of the cube

to find the diagonal we first need to find the diagonal of the bottom

So we can use pythagorean theorem

Let the diagonal of bottom face = x

So

$x^2 = 17^2 +17^2 = 289 + 289= 578 = 24.04$

Now this is the diagonal of the bottom face ,

Now we have to find the diagonal from the bottom face to the upper face .

Because bat can fit touching bottom face on one corner and touching upper face on opposite corner.

So again we apply the pythagorean theorem

let that diagonal be y

$y^2 = 17^2 +24.04^2 = 289+577.9216=866.9216 = 29.4435$

Still we get 29.445

Which means 0.6th part of the bat will still remain outside , and it won't fit in the cube.