Geometry Modeling 3d Quiz with Answers – Free PDF

Contents

This geometry modeling 3d quiz asks 10 multiple-choice questions on cross sections, solids of rotation and geometric modeling, and each answer comes with a short explanation.

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.

GeometryCommon Core: G-GMD.B.4 · G-MG.A.1 · G-MG.A.2 · G-MG.A.3

🎯 Cross Sections, Solids of Rotation and Geometric Modeling – Geometry math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

A plane cuts a cylinder parallel to its bases. What is the shape of the cross section?

A horizontal cut.

A A circle

B A rectangle

C A triangle

D An 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.

A A circle

B A rectangle

C A triangle

D A 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?

A A cylinder

B A cone

C A sphere

D A 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?

A 70 people per square mile

B 7,000 people per square mile

C 700 people per square mile

D 56,700 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?

A 960 BTUs

B 600 BTUs

C 4,800 BTUs

D 2,400 BTUs

Question 8

Which whole-number dimensions give a rectangular garden the greatest area using exactly 36 feet of fence?

A 6 ft by 12 ft

B 8 ft by 10 ft

C 4 ft by 14 ft

D 9 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!

0 / 10

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.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.