Unit 3: Area and Volume
Name: ________________
Teacher: _________
Period: ______
1
AIM: SWBAT to find the volume of a prism and pyramid.
Volume: the amount of space a 3-dimensional object holds.
FORMULAS
V = Bh, where B is the area of the base and h is the height of the solid
Right Rectangular Prism V = Bh
Cube
V= Bh
Right Triangular Prism
V= Bh
V =
V =
V =
h
Rectangular Pyramid
V=
Bh
3
OR V =
1
Bh
3
V=
2
CW: Find the volume of each solid. Show all work step-by-step, including the formula.
1)
2)
3)
V = Bh
4)
5) Find the volume of the right rectangular prism with a length of 36 cm, a width of 23 cm and
a height of 10 cm.
6) A container in the shape of a triangular prism is designed to hold pizza slices. The base of
the triangular lid is 7 inches long, the height is 11 inches, and the container is 3 inches deep.
What is the volume of the container to the nearest cubic inch?
3
HW: Find the volume of each solid. Show all work step-by-step, including the formula.
1)
4)
2)
3)
5) Find the volume of a rectangular prism with a
length of 16 in., width of 8 in., and height of 10 in
6) A glass pyramid constructed outside the Louvre Museum in Paris has a square base with a
side measurement of 35 meters and a height of 20.6 meters. Find to the nearest cubic meter,
the volume of this pyramid.
4
Do Now:
1) Is a circle a polygon? Why or why not?
2) State the formula for finding the circumference of a circle.
3) State the formula for finding the area of a circle.
4) What is the difference between circumference and area?
5) What type of number is π (Rational or Irrational) and why?
6) Find the area and circumference of the following, find the exact (leave your answer in
terms of π) answer and the approximate answer. (Round to the nearest tenth)
7) The circumference of a circle is 36π. Find the diameter and the radius of the circle.
5
AIM: SWBAT to find the volume of a cylinder, cone and sphere.
Volume: the amount of space a 3-dimensional object holds.
FORMULAS
V = Bh, where B is the area of the base and h is the height of the solid.
Right Circular Cylinder
(Exact & Approximate)
V = πr2h
Cone
(Exact & Approximate)
πr 2h
V=
3
Sphere
(Exact & Approximate)
4
V = πr 3
3
Find the EXACT and APPROXIMATE volume of each of the following. Round to the nearest
tenth when necessary.
1)
2)
3)
Exact Volume _________
Exact Volume _________
Exact Volume _________
Approximate Volume _____
Approximate Volume _____
Approximate Volume _____
6
4)
5)
6)
Exact Volume _________
Exact Volume _________
Exact Volume _________
Approximate Volume _____
Approximate Volume _____
Approximate Volume _____
7) Baseballs used in major league baseball have diameters that range between 2.76 inches and
2.94 inches. What is the difference in the exact volume between the largest and the smallest
baseball?
8) A party hat has the shape of a cone. The volume of the hat is 419 cm3. If the hat has a
height of 16cm, what is the measure of the radius to the nearest centimeter?
7
HW: Find the EXACT and APPROXIMATE volume of each of the following. Round to the nearest
tenth when necessary.
1)
2)
3)
Exact Volume _________
Exact Volume _________
Exact Volume _________
Approximate Volume _____
Approximate Volume _____
Approximate Volume _____
4) A history teacher has a spherical globe with a diameter of 14 inches. What is the EXACT
volume of the globe?
5) A cylinder has a volume of about 500 cm3 and a height of 10 cm. What is the length of the
radius to the nearest tenth of a meter?
6) Find the height of a cone to the nearest tenth if the radius is 5 inches and the volume is 487
in3.
8
Do Now:
1) To the nearest cubic meter, what is the volume of a cone with a radius of 3m and a height
of 4m?
a) 113m3
b) 12m3
c) 36πm3
d) 38m3
2) An official basketball approved by the National Basketball Association has a diameter of 9.4
inches. To the nearest square inch, what is the volume of this basketball?
a) 1,217in3
b) 138πin3
c) 435in3
d) 3,479in3
3) Find the exact volume of a cylinder that has a diameter of 22 in and a height of 22 in.
a) 10,648 in3
b) 2,662π in 3
c) 2,662 in 3
d) 8,363π in 3
4) A rectangular prism and a pyramid have a length of 5in, width of 9in, and a height of 10in.
Which has the greater volume? How much greater is it?
REVIEW: Area & Volume
Find the Exact and Approximate circumference and area of each circle. Show ALL work!!
Round your answer to the nearest tenth
1)
2)
36 ft
21 m
Exact Circumference ______________
Exact Circumference ______________
Approximate Circumference ____________
Approximate Circumference ___________
Exact Area _____________
Exact Area _____________
Approximate Area _____________
Approximate Area _____________
9
Answer each of the following. Be sure to SHOW WORK!
3) If the diameter of a circle is 15 ft, what is the radius of the circle? __________ ft.
4) Find the diameter of a circle whose circumference is 18.85 ft. Round your answer to the
nearest foot.
5) Find the width of a rectangle if the area is 24 square inches and the length is 8 in.
6) What is the surface area of rectangular prism with a width of 5 in., length of 12 in. and
a height of 8 in.? (SHOW WORK!)
SA = 2wl + 2lh + 2wh
7) A store keeps about 240 boxes of crayons in its inventory. If each box of crayons
measures 6 inches by 2.5 inches by 4 inches, how many cubic inches is needed to store all of
the boxes in its inventory?
8) Suppose you want to buy concrete for a 36 ft by 24 ft by 9 ft patio. If concrete costs
$55 per ft3, how much will the concrete for the patio cost?
10
9) A cylindrical storage tank has a diameter of 6m and a height of 5m. What is the EXACT
volume of the storage tank?
Find the volume of each of the following; show all work step – by – step. Round to the nearest
tenth when approximating.
10)
11)
12)
13)
14)
15)
Exact Volume ____________ Exact Volume ____________
Exact Volume ____________
Approximate Volume _______ Approximate Volume_______
Approximate Volume_______
11
16)
17)
Exact Volume ____________
Exact Volume ____________
Approximate Volume_______
Approximate Volume_______
18) What would the volume, to the nearest tenth, be in question #16 if you had half a sphere?
Show your work.
19) Find the Exact and Approximate volume of the hemisphere below.
Exact Volume: ___________
Approximate Volume: _____________
28 m
12