Cross Sections, Solids of Rotation and Geometric Modeling: Geometry Math Quiz – PDF Download
Answer these 10 multiple-choice questions on cross sections, solids of rotation, density and design. Pick one answer for each question and read the explanation to see the common mistake.
🎯 Cross Sections, Solids of Rotation and Geometric Modeling – Geometry math quiz
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Question 1
A plane cuts a cylinder parallel to its bases. What is the shape of the cross section?A horizontal cut.
AA circle
BA rectangle
CA triangle
DAn ellipse that is not a circle
Question 2
A plane passes through the apex of a cone and the center of its base. What is the cross section?A vertical cut.
AA circle
BA rectangle
CA triangle
DA trapezoid
Question 3
A sphere has a radius of \(5\text{ cm}\). A plane cuts it \(3\text{ cm}\) from the center. What is the area of the circular cross section?
A\(34\pi\text{ cm}^{2}\)
B\(25\pi\text{ cm}^{2}\)
C\(4\pi\text{ cm}^{2}\)
D\(16\pi\text{ cm}^{2}\)
Question 4
Which solid is made by rotating a rectangle about one of its sides?
AA cylinder
BA cone
CA sphere
DA cube
Question 5
A right triangle with legs \(3\text{ cm}\) and \(4\text{ cm}\) is rotated about the \(3\text{ cm}\) leg. What is the volume of the solid?Rotate the shape about the dashed axis.
A\(12\pi\text{ cm}^{3}\)
B\(16\pi\text{ cm}^{3}\)
C\(9\pi\text{ cm}^{3}\)
D\(48\pi\text{ cm}^{3}\)
Question 6
A district has 6,300 people in \(9\text{ mi}^{2}\). What is its population density?
A70 people per square mile
B7,000 people per square mile
C700 people per square mile
D56,700 people per square mile
Question 7
A room is \(10\text{ ft}\) by \(12\text{ ft}\) with an \(8\text{ ft}\) ceiling and needs 5 BTUs per cubic foot. How many BTUs are needed?
A960 BTUs
B600 BTUs
C4,800 BTUs
D2,400 BTUs
Question 8
Which whole-number dimensions give a rectangular garden the greatest area using exactly 36 feet of fence?
A6 ft by 12 ft
B8 ft by 10 ft
C4 ft by 14 ft
D9 ft by 9 ft
Question 9
A round hay bale is modeled as a cylinder with a diameter of \(5\text{ ft}\) and a width of \(4\text{ ft}\). What is its volume?
A\(100\pi\approx 314.16\text{ ft}^{3}\)
B\(25\pi\approx 78.54\text{ ft}^{3}\)
C\(10\pi\approx 31.42\text{ ft}^{3}\)
D\(50\pi\approx 157.08\text{ ft}^{3}\)
Question 10
A cube with an edge of \(3\text{ cm}\) has a mass of \(24.3\text{ g}\). What is its density?
A\(8.1\text{ g/cm}^{3}\)
B\(0.9\text{ g/cm}^{3}\)
C\(2.7\text{ g/cm}^{3}\)
D\(72.9\text{ g/cm}^{3}\)
🎉 Quiz complete!
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Remember:
Standards G-GMD.B.4, G-MG.A.1, G-MG.A.2 and G-MG.A.3 cover cross sections, rotations, modeling, density and design problems.
A plane parallel to the base of a cylinder, cone or sphere makes a circle; through the axis it makes a rectangle or triangle.
A rectangle spins into a cylinder, a right triangle into a cone, and a semicircle into a sphere.
Density = amount ÷ area or volume, such as people per square mile or BTUs per cubic foot.
Design problems pick the best option that satisfies constraints on size, material or cost.
