A rectangular solid has dimensions 4 x 5 x a. If the volume is 100, what is the measure of a, what is the surface area, and what is the length of the diagonal?

Question

Please help, I have no idea how to solve this.

Answer 1

First find a. 

 

You will need to find create an equation for the equation of a rectangular solid. 

 

l x w x h = V

 

With our problem it will be, 

 

4 x 5 x a = 100.      We wil simplify and solve for a.

 

20a = 100.

 

a = 5.

 

Now use it to find surface area. You will need the formula for surface area. 

2xarea of the Base + Perimeter of the Base x Height 

 

We will assume that the base is 4 by 5 with the height of 5.

 

so the equation (2 x (4x5)) + (4+5+4+5) x 5  

 

Simplified is 40 + 90 = 130 sq. units

 

The diagonal is a little more difficult to find. we are creating a line from one top corner to the bottom opposite corner.

first we find the diagonal of the flat rectangle base using Pythagorean theorem.  4² + 5² = C² which is 16+25 = C²

so C = sqroot 41. 

 

Then we use this number and the height to find the diagonal of the solid with the Pythagorean Theorem again.

5²+sqroot41² = C²

simplified is 25 + 41 = C²

C²=66

 

C = sqroot 66