SOLUTION: 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 siz

Algebra ->  Surface-area -> SOLUTION: 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 siz      Log On


   

Question 1137216: 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)
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Answer by MathLover1(20849) About Me  (Show Source):
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If the value of
a+=18.0
b+=1.2+
c+=5.0+
what is the surface area of this shape? (Use 3.14 as the value of pi)

the surface area of this shape will be sum of:
3 faces of the cube side length of a: 3a%5E2 (these faces have no cuts)
2 faces (upper and one on the left side of big cube) have cut of b%5E2 and area is: 2%28a%5E2-b%5E2%29
1+face (front) has a cut of b%5E2 and circle, so area is: a%5E2-%28b%5E2%2B2c%2Api%29
and, add surface area of three faces of small cube side length b:3b%5E2
surface_+area=3a%5E2%2B2%28a%5E2-b%5E2%29%2Ba%5E2-%28b%5E2%2Bc%5E2%2Api%29%2B3b%5E2

surface_+area=972%2B2%28324-1.44%29%2B324-%281.44%2B78.5%29%2B3%2A1.44
surface_+area=972%2B645.12%2B324-79.94%2B3%2A1.44
surface_+area=1865.5

or, since we have first deducted b%5E2 from three faces, then added same as faces of small cube, surface area is same as surface area of cube side length a minus area of the circle
surface_+area=++6a%5E2-c%5E2%2Api=6%2A18%5E2-25%2A3.14=1865.5