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

Answer:

Diameter of smallest circular opening = 12.81 in

Step-by-step 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,

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

$d=\sqrt{W^{2} +L^{2} }$

$d=\sqrt{10^{2}+8^{2}}$

$d=\sqrt{100+64}$

$d=\sqrt{164}$

$d=12.81\ in.$

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

Therefore diameter of smallest circular opening = 12.81 in.