Quick Checks
CCSS Math Grade 8 (G7 accelerated): 8.G.C
Cylinders, Cones, and Spheres (Form A)
8.G.C.9
Teacher Rationale
QCE79992
© 2016-2017 Amplify Education, Inc. All Rights Reserved.
Rationale: CCSS Math Grade 8 (G7 accelerated): 8.G.C Cylinders,
Cones, and Spheres (Form A)
Test Definition File
QCE79992
Item #
Correct Answer(s)
1
C
2
A
3
B
4
A
5
D
6
See Scoring Rubric
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© 2016-2017 Amplify Education, Inc. All Rights Reserved.
Rationale: CCSS Math Grade 8 (G7 accelerated): 8.G.C Cylinders,
Cones, and Spheres (Form A)
Rationale
Question #1 (E170380)
MA.8.G.C.9 > DOK 2
The radius of a cone is 8 inches. Its height is 15
inches. What is the approximate volume of the
cone?
Know the formulas for the volumes of cones, cylinders,
and spheres and use them to solve real-world and
mathematical problems.
A
B
C
D
Answer Choice Rationales
125.6 cubic inches
A. This answer results from neglecting to square the
radius and evaluating (1/3)(3.14)(8)(15) = 125.6
B. This answer results from multiplying 8 by 2 instead
of squaring 8, or from dividing the radius by 2
before using the formula.
C. Correct: The volume of a cone is given by the
formula V = (1/3)πr2h. Since r = 8 and h = 15,
the volume is (1/3)(3.14)(64)(15) ≈ 1005
cubic inches.
D. This answer results from neglecting to multiply by
the 1/3 in the formula (that is, using the formula for
the volume of a cylinder).
251.2 cubic inches
1005 cubic inches
3014 cubic inches
Question #2 (E170382)
MA.8.G.C.9 > DOK 3
The circular base of a cylinder has a
circumference of 31.4 feet. The height of the
cylinder is 12 feet. What is the approximate
volume of the cylinder?
Know the formulas for the volumes of cones, cylinders,
and spheres and use them to solve real-world and
mathematical problems.
A
B
C
D
A. Correct: To find the radius of the cylinder,
use the circumference formula C = 2πr, let C
= 31.4, and solve for r as follows: 31.4 = 2πr
→ r = 31.4 ÷ 2(3.14) → r ≈ 5. Then use the
formula for the volume of a cylinder: V = πr2h
→ V = (3.14)(5)2(12) → V ≈ 942 cubic feet.
B. This answer results from using the incorrect
formula for the volume for a cylinder and
multiplying the circumference times the height
times π: (31.4)(12)(3.14) = 1183
C. This answer results from using the diameter
instead of the radius in the cylinder volume formula
and solving V = (3.14)(100)(12 )= 3768
D. This answer results from using half the
circumference for the radius and solving V =
(3.14)(15.7)2(12) = 9288
942 ft3
1183 ft3
3768 ft3
9288 ft3
QCE79992
Answer Choice Rationales
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© 2016-2017 Amplify Education, Inc. All Rights Reserved.
Rationale: CCSS Math Grade 8 (G7 accelerated): 8.G.C Cylinders,
Cones, and Spheres (Form A)
Question #3 (E170381)
MA.8.G.C.9 > DOK 3
The volume of a sphere is 268 cubic meters.
What is its approximate diameter?
Know the formulas for the volumes of cones, cylinders,
and spheres and use them to solve real-world and
mathematical problems.
A
B
C
D
4.0 meters
Answer Choice Rationales
8.0 meters
A. This answer is the radius of the sphere; the radius
must be doubled to find the diameter.
B. Correct: The volume of a sphere is given by
the formula V = (4/3)πr3. Solve the equation
268 = (4/3)πr3, as follows: r3 = 340(3/4) ÷
(3.14) → r3 = 64.0 → r ≈ 4.0. The diameter is
twice the radius, so it is approximately 8.0
meters.
C. This answer results from solving πr3 = 268.
D. This answer results from solving (4/3)πr2 = 268.
8.8 meters
16 meters
Question #4 (E170384)
MA.8.G.C.9 > DOK 3
A cereal box is shaped like a cylinder with a
height of 7.4 inches. The volume of the cylinder
is 93 cubic inches. What is the approximate
radius of the cylinder?
Know the formulas for the volumes of cones, cylinders,
and spheres and use them to solve real-world and
mathematical problems.
A
B
C
D
A. Correct: Set V = 93 and h = 7.4 in the
cylinder formula formula V = πr2h, and solve
for r as follows: 93 = (3.14)r2(7.4) → r2 ≈ 4.00
→ r ≈ 2.0.
B. This answer results from failing to include pi in the
formula and setting volume equal to r2h: 93 =
r2(7.4) → r2 ≈ 12.6 → r ≈ 3.5.
C. This answer results from finding r2 and neglecting
to take the square root.
D. This answer results from multiplying by 3.14
instead of dividing when solving 93 = (3.14)r2(7.4)
finding r2 ≈ 39.4 → r ≈ 6.3.
2.0 inches
3.5 inches
4.0 inches
6.3 inches
QCE79992
Answer Choice Rationales
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© 2016-2017 Amplify Education, Inc. All Rights Reserved.
Rationale: CCSS Math Grade 8 (G7 accelerated): 8.G.C Cylinders,
Cones, and Spheres (Form A)
Question #5 (E170383)
MA.8.G.C.9 > DOK 3
A soccer ball was inflated from a radius of 10.0
centimeters to a radius of 11.0 centimeters.
What was the approximate increase in the
volume of the soccer ball?
Know the formulas for the volumes of cones, cylinders,
and spheres and use them to solve real-world and
mathematical problems.
A
B
C
D
A. This answer is obtained by using the correct
volume formula but making an error in evaluating
the difference in volumes by using the cube of the
difference in radius instead of the difference of
cubes of the radii: (4/3)(3.14)(11 – 10)3 = (4/3)
(3.14)(1) ≈ 4.19
B. This answer is obtained by using the incorrect
volume formula, V = (4/3)πr2.
C. This answer is obtained by finding the difference in
volumes using the incorrect volume formula, V =
πr3.
D. Correct: The sphere volume formula is V =
(4/3)πr3. The increase in volume is (4/3)
(3.14)(11)3 – (4/3)(3.14)(10)3 = (4/3)(3.14)
(113-103) = (4/3)(3.14)(1331 – 1000) = (4/3)
(3.14)(331) ≈ 1386.
4.19 cm3
87.9 cm3
1039 cm3
1386 cm3
QCE79992
Answer Choice Rationales
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© 2016-2017 Amplify Education, Inc. All Rights Reserved.
Rationale: CCSS Math Grade 8 (G7 accelerated): 8.G.C Cylinders,
Cones, and Spheres (Form A)
Question #6 (E170414)
MA.8.G.C.9 > DOK 3
The diagram shows a scoop of ice cream in a
cone. The scoop is shaped like a sphere with a
diameter of 6 centimeters.
Know the formulas for the volumes of cones, cylinders,
and spheres and use them to solve real-world and
mathematical problems.
4 Point Response:
The response demonstrates a high level of
understanding. A level 4 response is characterized by:
Show correct work in part A, similar to V = (4/3)πr3,
with r = 3 → V ≈ (4/3)(3.14)(33) ≈ 113 cubic
centimeters;
● Give the correct answer, 113 cubic centimeters, in
part A;
● Show correct work and and give a correct
explanation in part B, similar to "The volume of the
cone is given by the formula V = (1/3)πr2h, and the
radius of the cone is 3 centimeters. I set the volume
of the cone equal to 36π (the volume of the sphere)
and solved for h: (1/3)π(3)2h = 36π → 3πh = 36π →
h = 12 centimeters";
● Give the correct answer, 12 centimeters, in part B.
3 Point Response:
The response demonstrates a strong understanding,
but the work contains minor errors. A level 3 response
is characterized by:
●
A. Find the volume of the scoop of ice cream to
the nearest cubic centimeter. Show your work.
B. When the ice cream is pushed into the cone, it
exactly fills the cone with none of the ice cream
showing above the edge of the cone. What is the
height of the cone? Show your work and explain
how you found your answer.
●
●
●
●
Show work for part A that is incomplete or contains
one or two minor errors;
Give an answer for part A that is correct or
completely consistent with the minor errors in the
shown work;
Show work and give an explanation for part B that
are incomplete or contain one or two minor errors;
Give an answer for part B that is correct or
completely consistent with the minor errors in the
shown work.
2 Point Response:
The response demonstrates a basic but incomplete
understanding. A level 2 response is characterized by:
●
●
Show work and give an answer for part A that are
basically correct but may be incomplete and
include one or more minor errors;
Show work, and give an explanation and an answer
for part B that are basically correct but may be
incomplete and include one or more minor errors.
1 Point Response:
The response demonstrates minimal understanding. A
level 1 response is characterized by:
●
●
QCE79992
Show work and give an answer for part A that are
incomplete or contain one or more major errors, but
are not completely incorrect;
Show work, and give an explanation and an answer
for part B that are incomplete or contain one or
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© 2016-2017 Amplify Education, Inc. All Rights Reserved.
Rationale: CCSS Math Grade 8 (G7 accelerated): 8.G.C Cylinders,
Cones, and Spheres (Form A)
more major errors, but are not completely
incorrect.
0 Point Response:
There is no response, or the response is off topic.
QCE79992
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