Volume and Surface
Area of 3-D Shapes
VOLUME
• Volume is the measure of space inside a
3-D object.
• Imagine filling the classroom with boxes
measuring 1 cubic foot. How much would
we use?
• Area of the base x height = volume of a
prism or cylinder
• (Area of the base x height) ÷ 3 = volume
of a pyramid
SURFACE AREA
• Surface area is the measure
of all faces on a 3-D object.
• Imagine covering the floor,
walls, and ceiling of this room
with tiles measuring 1 square
foot. How many would we
use?
• Surface Area = sum of areas
of all faces and bases
Mary wants to fill the box below with candy hearts and then
wrap the box in Valentine’s paper. The box is 6 inches long, 6
inches wide, and 12 inches high.
Each pack of candy is 3 cubic inches. How many packs of candy
will she need?
She has a piece of wrapping paper that is 500 square inches. Will
that be enough? Will there be any wrapping paper left over?
V = 6 x 6 x 12 = 432 cubic inches
432 ÷ 3 = 144 packs of candy
SA = 2(6x6) + 2(6x12) + 2(6x12) =
360 square inches
500 – 360 = 140 square inches left
Bill is working on a farm for the summer. He is told by Farmer Brown to remove the
top of the silo, fill it with grain, and then paint the outside of the silo to match the
barn. The silo is 30 feet tall, and 6 feet across the top.
One acre of harvested grain is 64 cubic feet. Bill estimates it will take 10 acres of
harvested grain to fill the silo. Is his estimate accurate? Why/why not?
One can of red paint will cover 100 square feet. How many cans of red paint will Bill
need?
V = ∏r2h
V = 3.14 x 3 x 3 x 30
Volume = 847.8 cubic feet
64 x 10 = 640
847.8 – 640 = 207.8 cubic feet of space left over. Bill needs
about 13 acres of harvested grain to fill the silo.
SA = area of 2 circles + area of rectangle. ∏r2= 3.14 x 3 x 3 = 28.26 square feet
The rectangle is wrapped around the circle, so its length is the circumference of
the circle. C = ∏d = 3.14 x 6 = 18.84
A = lw = 18.84 x 30 = 565.2 square feet
SA = 28.26 + 28.26 + 565.2 = 621.72 square feet
Bill needs 7 cans of paint, because 6 cans
will only cover 600 square feet.
A theme park is creating a new statue to honor the recently deceased
Mr. Tour I. Angle. You are on the planning committee. The designs
available are a triangular prism and a square pyramid. The statues will
need to be painted and filled with concrete.
The triangular prism would have a 12 foot-long base, stand 8 feet tall,
and be 8 feet thick with a slant height of 10 feet.
The square pyramid would have an equilateral base of 12 feet, and
stand 8 feet tall with a slant height of 10 feet. Each face height would
be 8 feet.
A $20 can of paint will cover 100 square feet. A cubic foot of
concrete costs $5. How much will each statue cost? Which is the best
choice, if the park is trying to save money?
Prism V = (½ bh)h = 48 x 8 =384 cubic feet
384 x$5 = $1920
Prism SA = area of 2 triangles + area of 3 rectangles =
48+48+96+80+80 = 352 square feet
$20 x 4 = $80
Pyramid V = lwh ÷ 3 = 384 cubic feet
384 x$5 = $1920
Pyramid SA = area of 4 triangles + area of square base =
48+48+48+48+144 = 336 square feet $20 x 4 = $80
HOMEWORK ASSIGNMENT
• Write your own word problem
involving volume and surface area.
• You may not use one of the previous
examples.
• If you bring a visual aid to go with
your problem, you will receive extra
credit.