Cube Surface Area

[ganjum2671]

A cube of side length a is modified by cutting a cubic shape of side length b from one of it's corners. In addition a cylindrical hole is cut through the shape with a radius of size c. If the value of a is 18.0, b is 1.2 and c is 5.0, what is the surface area of this shape? (Use 3.14 as the value of pi)

 

[MarkFL]

First, I would observe that cubic shape cut does not alter that surface of the large cube...the new surfaces exposed are equal to the surfaces removed. So, we only have to deal with the cylindrical cut, which removes two circular surfaces and adds the lateral surface of the cylinder.

So, I would first note the surface of the cube before the cylindrical cut is \(6a^2\). Then we subtract:

[MATH]2\pi r^2[/MATH]
And then we add:

[MATH]2\pi ra[/MATH]
What do you get?

 

[ganjum2671]

The entire cube has a surface area of 1,944 and after substituting the radius into the first equation you get 157 (I replaced pi with 3.14) and the second equation is equal to 565.2. Subtracting 157 from 1,944 you get 1787 and adding the 565.2 back you get 2352.2. Which is correct! Thank you so much for all your help! It's much appreciated and I wish I could do something to return it!! Also why doesn't the cube being cut out matter?

 

[MarkFL]

...why doesn't the cube being cut out matter?

I saw it by imagining the vertical surfaces swinging out 90° and the horizontal surface rising to the top of the cube, but we can just as easily observe that an area of \(3b^2\) was removed, but \(3b^2\) was created, so the net effect on the surface was no change at all.