This geometry volume formulas quiz asks 10 multiple-choice questions on area and volume formulas, and each answer comes with a short explanation.
Answer these 10 multiple-choice questions on circle formulas, Cavalieri's principle and volumes of cylinders, pyramids, cones and spheres. Choose one answer for each question, then read the explanation.
GeometryCommon Core: G-GMD.A.1 · G-GMD.A.3
🎯 Area and Volume Formulas – Geometry math quiz
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Question 1
What is the circumference of the circle?A circle with radius 5 in.
A\(25\pi\text{ in}\)
B\(5\pi\text{ in}\)
C\(10\pi\text{ in}\)
D\(20\pi\text{ in}\)
Question 2
What is the area of a circle with a diameter of \(12\text{ cm}\)?
A\(144\pi\text{ cm}^{2}\)
B\(12\pi\text{ cm}^{2}\)
C\(36\pi\text{ cm}^{2}\)
D\(72\pi\text{ cm}^{2}\)
Question 3
Which statement is Cavalieri's principle?
ASolids with equal heights and equal cross-sectional areas at every level have equal volumes.
BSolids with equal heights always have equal volumes.
CSolids with equal surface areas always have equal volumes.
DSolids with equal base perimeters have equal volumes.
Question 4
What is the volume of the cylinder?A cylinder, r = 3 in, h = 5 in.
A\(15\pi\text{ in}^{3}\)
B\(30\pi\text{ in}^{3}\)
C\(75\pi\text{ in}^{3}\)
D\(45\pi\text{ in}^{3}\)
Question 5
What is the volume of the rectangular pyramid?A pyramid with a 6 cm by 4 cm base.
A\(216\text{ cm}^{3}\)
B\(72\text{ cm}^{3}\)
C\(108\text{ cm}^{3}\)
D\(24\text{ cm}^{3}\)
Question 6
A cylinder has a volume of \(90\pi\text{ cm}^{3}\). A cone has the same radius and the same height. What is the volume of the cone?
A\(270\pi\text{ cm}^{3}\)
B\(45\pi\text{ cm}^{3}\)
C\(30\pi\text{ cm}^{3}\)
D\(60\pi\text{ cm}^{3}\)
Question 7
What is the volume of a sphere with a radius of \(3\text{ cm}\)?
A\(36\pi\text{ cm}^{3}\)
B\(12\pi\text{ cm}^{3}\)
C\(27\pi\text{ cm}^{3}\)
D\(108\pi\text{ cm}^{3}\)
Question 8
The radius of a sphere is doubled. By what factor does its volume increase?
AIt is multiplied by 2.
BIt is multiplied by 4.
CIt is multiplied by 6.
DIt is multiplied by 8.
Question 9
A circle with radius r is cut into sectors and rearranged as shown. What is the length of the base of the new shape?Rearranged sectors.
AThe whole circumference, 2πr
BHalf the circumference, πr
CThe diameter, 2r
DThe radius, r
Question 10
A cone has a radius of \(6\text{ cm}\) and a volume of \(48\pi\text{ cm}^{3}\). What is its height?
A\(\frac{4}{3}\text{ cm}\)
B\(8\text{ cm}\)
C\(12\text{ cm}\)
D\(4\text{ cm}\)
🎉 Quiz complete!
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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
Standards G-GMD.A.1 and G-GMD.A.3 cover informal arguments for circle and solid formulas, and solving volume problems.
Circumference C = 2πr and area A = πr² both come from the constant π = C/d.
Cavalieri’s principle: equal heights and equal cross-sectional areas at every level mean equal volumes.
Cone and pyramid volumes are one third of the matching cylinder or prism: V = (1/3)Bh.
Sphere volume V = (4/3)πr³ equals two hemispheres, each a cylinder minus a cone.
How to use this geometry volume formulas quiz
Retake this geometry volume formulas quiz until every answer is right, then move on to the worksheet and the test.
