Wow. This is complicated. It's not hard ... it just has a lot of steps to it.
-- The top, round surface, where the cups and glasses sit:
A circle. The area of a circle is (pi) (radius)²
= (3.14) (24 inches)²
= (3.14) (576 square inches)
= 1,808.64 square inches
-- The 8-inch edge around the table-top.
This is actually a long skinny rectangle, wrapped around it.
The width of the rectangle is 8 inches.
The length of the rectangle is the circumference of the table-top.
Circumference of a circle = (pi) (diameter)
= (pi) (2 x radius)
= (3.14) (48 inches)
= 150.72 inches
Area of the long skinny rectangle = (8 inches) x (150.72 inches)
= 1,205.76 square inches .
-- Legs.
Each leg is a rectangular prism.
Area of the bottom of the leg, where it stands on the floor
= (2.5 inches) x (2.5 inches) = 6.25 square inches
Area of each of the 4 sides =
= (10 inches) x (2.5 inches) = 25 square inches
Area of the top of the leg: glued to the table-top; not stained.
Total surface area of each leg = (6.25 + 25) = 31.25 square inches)
Surface area of all 4 legs = (4) x (31.25) = 125 square inches.
So far, we have:
-- table-top . . . . . . . . . . . . 1,808.64 square inches
-- strip around table-top . . 1,205.76 square inches
-- 4 legs . . . . . . . . . . . . . . . 125 square inches
Total 3,139.4 square inches
This is not one of the choices.
Did I miss something ?
What about the underside of the tabletop ?
That's (the same area as the top of the table-top)
minus
(the 4 little squares where the legs are glued on) .
Let's try that.
Area of the full round surface of the table-top = 1,808.64 square inches
... Each little square
where a leg is glued on = (2.5 x 2.5) = 6.25 sq inches.
Four of them = (4 x 6.25) = 25 square inches
Area of the part of the underside that needs to be stained =
(1,808.64 - 25) = 1,783.64 square inches
So now we have:
-- top surface of the table-top. . . . . 1,808.64 square inches
-- strip around table-top . . . . . . . . . . 1,205.76 square inches
-- bottom surface of the table-top . . 1,783.64 square inches
-- 4 legs. . . . . . . . . . . . . . . . . . . . . . . 125 square inches
Total: 4,923.04 square inches
At this point, I'm going to pull a fast one on you, and talk to you
like the Engineer that I am. You might not like it.
This answer that I have is not exactly the same as any of the choices.
But it's only 12.5 square inches (0.25%) less than one of them.
So now I'm going to say:
-- the choice of 4,935.54 must be the correct one;
-- I must have made a small arithmetic error somewhere, but
I believe I worked the problem correctly; and
-- I've already spent enough time on this one to earn 5 points,
and I'm not going to spend any more of it.
