Question

Suppose you have a rectangular shipping box that measures 30 cm × 15 cm × 20 cm. What is the longest length of a 1 cm diameter wooden dowel that could fit inside the box? (round to the nearest whole centimeter)

Plz hurry i need it before 12:40pm
1-22-18

Answer 1

Answer: 39 cm

SOLUTION

Given,

Length, L = 30 cm

Breadth, B = 15 cm

Height, H = 20 cm.

The longest length of a 1 cm diameter wooden dowel that could fit inside the box = The diagonal, D of the box (from the lower front left corner to the upper back right corner)

Diagonal, D = ?

D^2 = L^2 + B^2 + C^2

D^2 = 30^2 + 15^2 + 20^2

D^2 = 900 + 225 + 400

D^2 = 1525

D = 39 cm (to the nearest whole centimeter)

Therefore, the longest length of a 1 cm diameter wooden dowel that could fit inside the box is 39 cm (to the nearest whole centimeter).

Answer 2

The longest length of dowel will feet in the dimension that will give us the highest length of the hypotenuse;
given that the dimension of our box is:
15 by 20 by 30:
this will be given by:
c^2=a^2+b^2+c^2
c^2=15^2+20^2+30^2
c^2=225+400+900
c^2=1525
c=√1525
c=39.05 cm
Therefore the longest dowel will be 39 cm (to the nearest whole centimeter)