Describe the vision for the world that president roosevelt suggests and explain what roosevelt wanted the united states to do to achieve that vision?

Two major reasons:
First off, a canal was a huge business boon to the US. Most Americans lived on the east coast, but huge opportunities existed on the west. The naval trip around the southern tip of South America added 8,000 miles to a trip.  By creating a canal, the US could control the flow of goods and services between the hemispheres.  This was critical to TR's vision of the US as a world power.

Secondly, he believed in a large US Navy as a way of extending US power. In the war against Spain, the delay for ships to pass around the southern tip seriously impacted the American ability to exert power. A canal allowed us to build and manage freely flowing naval resources. He built the Great White Fleet to exert this power.

Realize that TR set the US on the course towards an Empire. Building the canal required him to run roughshod over international law, supporting a revolution in Panama from Columbia. The American presence in Panama established the US as a hemisphere power. https://www.quora.com/Why-did-president-Theodore-Roosevelt-want-the-United-States-to-build-the-Panam...

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