Why It Matters: Geometry

Why use measurements and geometric equations to analyze shapes and structures?

Tom, a carpenter at the Monterey Bay Aquarium, is busy putting in a new installation. It’s one of the biggest fish tanks in the world, and the idea behind it is to make guests feel as if they’re actually in the tank, surrounded by colorful sea life. Visitors will be able to walk on a glass floor with tropical fish beneath them, while more tropical fish swim in a tank overhead. The floor and ceiling tanks will be connected by a huge glass column tank in the middle of the room. Tom is excited for the installation to open because he knows visitors are going to be in awe when they experience it!

Tropical fish swimming under water, through undersea plant life and coral

How much water does it take to fill a huge fish tank?

The tanks are in place, and now Tom has to tell his supervisor how much water they’ll need to fill them, in cubic feet. How can Tom figure this out?

He knows that the floor tank and the ceiling tank have the same dimensions: they’re each 10 meters long, 6 meters wide, and 1.5 meters deep. The cylinder connecting them is 7 meters high, with a radius of 2 meters. How much water will it take to fill all three tanks?

Once the tanks are filled, Tom also needs to install a protective clear coating on the glass to make sure it doesn’t get scratched or damaged by visitors. How much of the clear coating will he need to cover the surfaces of all the tanks?

To solve these problems, Tom will rely on his knowledge of geometry, volume, and surface area. Read on to find out how you can use these concepts to solve real-world problems like Tom’s.