Exploring maths through problem solving

Problem of the Week

Bagging Your Dog

Dogs are allowed on the New York subway as long as the dog is in a bag. How much material would you need to make a bag like this one for your dog? My dog is only small – 30 cm up to her shoulder, 32 cm long (neck to tail) and 16 cm thick (across the shoulders).


This bag looks to be an open rectangular prism because one face is missing.

The area of the rectangular base needs to be the shoulder width of my dog (16 cm) multiplied by her length (32 cm).

This base therefore has an area of 16 cm x 32 cm = 513 cm2


The perimeter of the base is 2 x (16 + 32) cm = 96 cm

The perimeter multiplied by the shoulder height of my dog (30 cm) gives the area needed for the side faces.

This area is 96 cm x 30 cm = 2 880 cm2


Altogether the area is 513 cm2 + 2 880 cm2 = 3393 cm2


I would also need to add material for the seams and for the straps of the bag.

To be safe, I would buy about 5000 cm2 of material, which is 5000/10 000 m2 = 0.5 m2

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