Could someone please help me with these two math questions?

Question

1. A climber is standing at the top of Mount Kazbek, approximately 3.1 mi above sea level. The radius of the Earth is 3959 mi. What is the climber's distance to the horizon? (Round answer to nearest tenth.)

2. A tank in the shape of a rectangular prism measures 7 dm by 4 dm by 10 dm. The tank is completely filled with 10,690.4 L of liquid. What is the density of the liquid?


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If someone could help me, it would be very appreciated!

Answer 1

1.  Draw a diagram with the line of sight drawn from the top of the mountain to the horizon.  This line is tangential to the surface of the earth (assuming the earth is a nice round ball) and so it is perpendicular to the radius line drawn from the center of the earth to the horizon point.  The distance to the top of the mountain from the center of the earth is the third side of a right angle triangle.  Can you solve the problem from there?

 

2. All you give here are the dimensions of the prism from which you can calculate its volume, and the volume of the liquid.  Is that meant to be the mass of the liquid instead of the number of liters (L)?  You can't answer it from this information.