NAME ____________________________________________ DATE _____________________________ PERIOD _____________
Practice 7.8(B)
SCORE __________
Explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid
having both congruent bases and heights and connect that relationship to the formulas.
Multi-Step Example
Kathy is making metal garden statues to sell at a craft show. One mold is a triangular prism with
base area 12 square feet and height 5 feet. The second mold is a triangular pyramid with the same
base and height dimensions. How many times greater is the volume of the triangular prism than the
triangular pyramid?
Determine the volume of the triangular prism.
12 • 5 = 60 cubic feet
Determine the volume of the triangular pyramid.
!
!
• 12 • 5 = 20 cubic feet
Divide to find the ratio of the volumes.
60 ÷ 20 = 3
So, the volume of the triangular prism is 3 times greater than the volume of the triangular pyramid.
1 What is the volume of a triangular pyramid with the
same base and height dimensions of the prism below?
2 Elaina is collecting coins for a fundraiser. She has two
coin banks to fill. One coin bank is in the shape of a
triangular prism. The other coin bank is in the shape of
a triangular pyramid. Both coin banks have the same
base and height measurements. The triangular prism
has a volume of 115 cubic inches. What volume of
coins can the triangular pyramid coin bank hold?
!
F 19 in!
!
!
A 19.25 in!
G 38 in!
B 38.5 in!
H 115 in!
C 57.75 in!
J 345 in!
!
D 115.5 in!
Course 2 • Expressions, Equations, and Relationships TX89 NAME ____________________________________________ DATE _____________________________ PERIOD _____________
Practice 7.8(B) (continued)
3 Pam has two fish tanks. Tank A is in the shape of a
triangular prism. Tank B is in the shape of a triangular
pyramid. How much water will it take Pam to fill both
tanks with water?
Tank
A
Base Area
B
9ft !
9 ft
!
Height
7 ft
7 ft
6 Rob has a clock shaped like a triangular prism with a
base measuring 24 square inches and a height of 7
inches. Dave has a clock in the shape of a triangular
pyramid with the same base and height dimensions.
Whose alarm clock would take up less space, and by
how much?
A They would take up the same space.
B Dave’s; 3 times the space of Rob’s
A 21 ft !
B 42 ft
SCORE __________
!
C Dave’s; the space of Rob’s
!
!
!
D Rob’s; the space of Dave’s
C 63 ft !
!
D 84 ft !
4 A triangular prism has base area 30 square meters and
height 7.5 meters. A triangular pyramid has the same
base area and same height. What is the total volume of
the figures?
7 Joyce has two pendants. One is in the shape of a
triangular prism with a base of 10 square centimeters
and a height of 1.5 centimeters. The second is in the
shape of a triangular pyramid with the same base and
height dimensions. How much gold was used to
make both pendants?
F 300 m!
F 5 m!
G 225 m!
G 10 m!
H 150 m!
H 15 m!
J 75 m!
J 20 m!
5 Claire built two sand sculptures, a triangular prism and
a triangular pyramid. The sculptures have congruent
bases and heights. The pyramid is shown. What is the
volume of the triangular prism sculpture, in cubic feet?
Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
value.
8 What is the difference in volume of the figure shown
and the volume of a triangular pyramid with the same
base and height dimensions?
A 40 m!
B 80 m!
C 120 m!
D 240 m!
TX90 Course 2 • Expressions, Equations, and Relationships
NAME ____________________________________________ DATE _____________________________ PERIOD _____________
Practice 7.8(B)
SCORE __________
Student Recording Sheet
Fill in the correct answer. For gridded-response questions, write your answers in the boxes on the answer grid and
fill in the bubbles to match your answers.
1
2
7
3
4
6
8
5
Course 2 • Expressions, Equations, and Relationships
TX91