Question

In this diagram, a rope is attached to a small pulley at the apex of an isosceles prism. What is the minimum length of the rope (r) needed to span the sides of the prism, rounded to the nearest whole number?

A.
5 units

B.
10 units

C.
12 units

D.
20 units

Answer 1

Explanation:

10 units for plato

Answer 2

Minimum length of rope needed to span the sides of the prism is 10 units.

Explanation:

Let us draw a perpendicular from apex to base BC,Let it be AD since ΔABC is isosceles triangle, that perpendicular will touch mid of base. That is BD=DC=
`(6)/(2)`=3

Now we know the angle m∠ABC as 53.13°.

From ΔADC,
`cos(53.13)=(DC)/(AC) =(3)/(((r)/(2) ))`

`cos(53.13)=(6)/(r)`

`r=(6)/(cos(53.13)) = 9.999`≈10

Hence minimum length of rope needed to span the sides of prism is 10 units.