Question

A rectangular box is 10 in. ​wide, 10 in. ​tall, and 8 in. long. What is the diameter of the smallest circular opening through which the box will​ fit?

Answer 1

Diameter of smallest circular opening = 12.81 in

Explanation:

Given:-

Width of rectangular box(W)=10 in.

Length of rectangular box(L)=8 in.

Height of rectangular box(H)=10 in.

For box to fit in the smallest circular opening we need to find the diagonal of the rectangular box, therefore

diagonal of rectangular box=diameter of smallest circular opening

So,

`Diagonal\ (d)=\sqrt{width^(2)+length^(2)  }`

`d=\sqrt{W^(2) +L^(2) }`

`d=\sqrt{10^(2)+8^(2)}`

`d=√(100+64)`

`d=√(164)`

`d=12.81\ in.`

`\therefore\ diagonal\ (d)=12.81\ in`

Therefore diameter of smallest circular opening = 12.81 in.