Curriculum 2.0 Geometry: Unit 3-Topic 1, SLT 13
Name:
Volume Stations Sample Answers
Date:
Period:
Golf Ball
Packages
1) A golf ball has a diameter of 1.68 inches and can be packed in two different ways, shown above. The
cylindrical package has a volume of 11.361in3 and a diameter of 1.6875in and the rectangular prism has
a base 1.6875 in. x 1.6875 in. If these two packages are the same height, find the volume of the
rectangular prism package.
1
1
d  (1.6875)  0.84375
2
2
2
Vcyl   r h
r
11.361   (0.84375) 2 h
h  5.080
Vprism  Bh  (1.6875)(1.6875)(5.080)  14.465
The volume of the rectangular prism is approximately 14.465 in3.
2) If each package holds 3 standard sized golf balls, how much unused space is there in each package?
Vballs  3(2.483)  7.449
Vcyl  11.361
11.361  7.449  3.912
Vprism  14.465
14.465  7.449  7.016
The volume of each golf ball is 2.483 in3. Based on the other dimensions, we know each package
can only fit three golf balls; the volume of three golf balls 7.449 in3. In the cylinder, 3.912 in3 of
volume are unused. The rectangular prism has approximately 7.016 in3 of unused volume.
Adapted from nyc.gov
Page 1 of 4
Curriculum 2.0 Geometry: Unit 3-Topic 1, SLT 13
Name:
Volume Stations Sample Answers
Date:
Period:
The Ancient Pyramids
1) Calculate the missing information for each of the pyramids based on the current measurements:
a. The Pyramid of Menkaure has a height of about 215 feet and a base side length of about 339 feet.
What is its volume?
1
1
Vpyr  Bh  (339)(339)(215)  8, 236, 005 ft 3
3
3
b. The Pyramid of Khafre has a volume of about 74,400,000 cubic feet and a base side length of 706
feet. What is its height?
1
Vpyr  Bh
3
1
74, 400, 000  (706)(706) h
3
h  447.801 ft
c. The Great Pyramid of Khufu has a volume of about 86,700,000 cubic feet and a height of 455 feet.
What is the length of its base?
1
Vpyr  Bh
3
1
86, 700, 000  s 2 (455)
3
2
s  571, 648.352 ft 2
s  756.074 ft
2) Over thousands of years, the pyramids have lost height and volume due to weathering and erosion.
a. The Great Pyramid of Khufu once stood 26 feet taller than it is today. Calculate the original volume
of the Great Pyramid.
1
1
Vpyr  Bh  (571, 648.352)(481)  91, 654, 285.77 ft 3
3
3
b. The Pyramid of Khafre was built with an original volume of 78,300,000 cubic feet. What was its
original height?
1
78,300, 000  (706)(706)h
3
h  471.274 ft
Adapted from nyc.gov
Page 2 of 4
Curriculum 2.0 Geometry: Unit 3-Topic 1, SLT 13
Name:
Volume Stations Sample Answers
Date:
Period:
Disposable
Cup
1
15
1) A tapered cup has a base radius of 1 inches and an opening radius of 1 inches. It has a height of
16
4
3
4 inches. Use what you know about proportional reasoning and the formula for the volume of a cone
4
to determine the volume of the liquid the cup is able to hold.
1.9375
5
2) A 12 ounce can of soda can hold 21.656 cubic inches of volume. How many cans of soda can fit in one
disposable cup?
38.492  21.656  1.777cans
Adapted from nyc.gov
Page 3 of 4
Curriculum 2.0 Geometry: Unit 3-Topic 1, SLT 13
Name:
Volume Stations Sample Answers
Date:
Period:
Quinceanera
Centerpieces
Yecenia is planning to create centerpieces for her quinceanera. Each centerpiece will be made from a cylindrical
glass vase that is 28 cm tall and has a radius of 6 cm. She will fill them half way with water, and then add
marbles until the water line is three-quarters of the way up the cylinder.
1) What volume of marbles will she need for each centerpiece?
Vcyl   r 2 h   (6)2 (28)  3166.725cm3
1
(3166.725)  791.681cm3
4
2) Each marble has a diameter of 22mm. Yecenia can buy bags of 100 spherical marbles for $4 per bag.
a. How many 22mm marbles will she need to make 30 centerpieces?
1cm3  1000mm3
4
(11)3   5575.279 mm3 / marble
3
791681mm3 / 5575.279mm3  141.998 marbles
She will need 4260 marbles (142 marbles per centerpiece).
b. How many bags will she need to buy? How much will it cost?
4260 100  42.6  43 bags
43  4  $172
3) Would it be cheaper to buy bags of 100 marbles, measuring 16mm in diameter, for $3 each? Defend your
answer using mathematics.
No. She would need 11,074 of the 16mm marbles (369 for each centerpiece) because of the size
difference. This means she would need 111 bags which would cost her $333.00.
Adapted from nyc.gov
Page 4 of 4