NAME:
DATE: ______/_______/_______
Math-8 NOTES
What: applying surface area . . .
Why: To investigate a variety of different types of surface area applications, including
real-life scenarios for surface area.
Key words for surface area problems:
Traditional surface area word problems:
Scenario
1) A jewelry box needs to be
painted on all sides. If it is 8 in
long, 3 in wide, and 3 in tall,
how many square inches
needs to be covered?
2) A cylindrical box needs to be
wrapped with the exact
amount of paper needed to
cover all of it, including the top
and bottom. If the radius is 2.5
in, and the height is 4.5 in,
what is its total surface area?
3) One of the pyramids in Egypt
needs to be treated with a
special preservation chemical
(floor included). The base of
the pyramid is a square with a
side length of 50 ft, and the
pyramid has a slanted height
of 60 ft. tall, how much of the
chemical will be needed?
Answer
4)
A modern art sculpture that is
cone-shaped needs to be
painted (bottom face
included). If the diameter of
the base is 8 ft, and the slanted
height is 10 ft, how much paint
will be needed?
What happens when the problem does not include the
entire surface area??
Sometimes a word problem will ask us for the surface area of a 3-D figure,
but will NOT include the top face, bottom face, etc.
Scenario
1) A wooden box will be painted,
however, the bottom face will
not be painted. If it is 6 ft long,
4 ft wide, and 5 ft tall, how
much surface area will be
painted?
2) A rectangle-based pyramid
sculpture will cleaned. Since it
is permanently affixed to the
floor, the bottom face can not
be reached. If the rectangle
base is 7 ft long, 5 ft wide, and
the slanted height is 12.5 ft,
how many sq. ft of the pyramid
will need to be cleaned?
3) An ice cream cone will be
coated with chocolate on its
outside surface only. If the
cone has a radius of 2 in and a
slanted height of 3.5 in, how
many square in of chocolate
will be needed?
Answer
DATE: ______/_______/_______
NAME: ____________________________
Traditional surface area word problems:
1. Darius is going to wrap a present that has the shape of a cone with a slant height of 12 inches and a
radius of 6 inches. How much wrapping paper will he use?
2. A roll of paper towels is 11 inches high and 6 inches in diameter. About how much plastic is needed to
wrap the roll?
3. A keepsake rectangular box will be covered in fabric on all sides. If the box is 14 inches long, 3.5
inches wide, and 2.5 inches tall, how much fabric will be needed?
4. Michele is going to wrap a present packed in a cylinder that has a radius of 4 inches and a height of 7
inches. How much wrapping paper will Michele need?
5. A triangular prism-shaped modern art sculpture will be painted on all sides. The triangle bases are
equal on all three sides– each side length is 8 feet long and the height of each of the triangle bases is 6.9
feet. The entire triangular prism sculpture is 10 feet tall. How much paint will be needed?
6. A rectangular pyramid-shaped toy will be wrapped with the exact amount of paper it takes to cover all
the faces. Its base has a length of 7 inches and a width of 2 inches. The slant height is 7 inches. How
much paper will be needed?
7. What is the surface area of a triangular pyramid that has a slant height of 14 feet, and a right triangle
base with sides that measure 5 feet, 12 feet, and 13 feet (Hint: Add the given measurements to the
below picture)?
Surface area with “missing” parts (faces):
8. Chelsea's basement is 18 feet long and 12 feet wide. The floor-to-ceiling height is 8 feet. There
are no windows in the basement. Chelsea will paint all four walls and the ceiling. She will not
paint the floor. How much paint will she need?
9. A potato chip can is shaped like a cylinder. It has a diameter of 3 inches and a height of 8.5
inches. What is the size of the label of the can that covers the curved surface?
10. Ethan built a case for his CD’s . He left the front of the case open so he could slide the CD’s in
and easily see the title of each one. How many square inches of wood did he use to make the
case?
11. A circular birthday cake will be frosted on all sides except for the bottom. If the diameter of
the cake is 12 inches and the height is 7 inches, how much frosting will be needed?
12. The outside of a square-based pyramid in Egypt will be treated with a special preservation
chemical. The floor will not be treated. If the square base has a side-length of 20.5 feet and the
pyramid is 50 feet tall, how much chemical will be needed?
13. The outside of a cone-shaped birthday hat will be covered with a festive fabric. The diameter
of the circle opening is 7 inches and the slanted height of the hat is 6 inches. How much fabric
will be needed?