Hints on assigned surface area challenge problems
The challenge problems I’m referring to are:
a) the hemisphere problems on the surface area of spheres & hemispheres sheet,
as well as #8 on the surface area of mixed shapes sheet
b) #2, 4, 5, 7, & 9 on the surface area of a cone sheet (the ones that show actual
height instead of slant height)
c) the lying down triangular prism problems #1, 4, and 6 on the surface area of prisms
sheet and #2 on the surface area of mixed shapes sheet
For surface area, except for cubes & rectangular prisms, the challenge problems aren’t
“backwards” problems. That’s because 1) you’re not likely to get anything that complicated
on the GED® test and 2) the procedure would be the same as the one for other “backwards”
problems you’ve been doing--write down the formula, plug in all known values, and then use
algebra or common sense to find the unknown value. Instead, the surface area challenge
problems are ones that make you stretch your critical thinking skills and perhaps figure out
what old tools to dig out of your math toolbox. Try the challenge problems yourself, and
then come back for some hints.
a) The trick with the hemisphere surface area problems is that there’s more to be done than
just dividing the surface area of a sphere in half. Notice the flat circular part of the
hemisphere. That’s one of the faces that has to be counted in surface area.
b) The formula for the surface area of a cone calls for slant height. However, the challenge
problems show regular height (h) instead of slant height (s). That’s not a mistake. It’s a
chance to stretch your brain. Look at #2 and see if you can figure out how to calculate slant
height from the information provided. Stop reading and think before continuing to the next
sentence……….. Give up? Notice that the height (h) and the radius of a cone make a 90
angle. Remember the Pythagorean theorem—a2 + b2 = c2? If you took the height squared
and added it to the radius squared, you’d get the slant height squared. If you took the
square root of that, it would be the slant height. Magic! (If you round off the calculated slant
height instead of saving all rounding ‘til the end, your answer will be slightly different from
the one on the answer key.)
c) The lying down triangular prism surface area problems don’t have any trick. They just test
your ability to keep track of lots of information. The p in the formula is the perimeter of the
Base. That’s not necessarily the perimeter of the bottom of the picture. If the diagram
shows a triangular prism lying on its side, the perimeter is the perimeter of that triangular
Base. The height in the formula is the height of the whole prism, not the little height of the
triangular Base. Remember that in a prism the height is the distance between the two
Bases. It’s not always pictured vertically. Finally, remember that capital B is the area of the
Base of the prism. That’s the area of the entire triangular Base, so it comes in square units.
It’s not the same as little “b,” the regular unit length of the line segment on one side of the
triangle.
D. Stark 5/2/2016