Geometry Modeling 3d Test with Answers – Free PDF

Contents

This geometry modeling 3d test checks cross sections, solids of rotation and geometric modeling in 45 minutes, with 8 questions for a total of 20 points.

This 45-minute test has 8 questions worth 20 points. Show every step and give exact answers in terms of $\pi$ unless a question asks for a rounded value. Include units in every answer.

Test information

Grade: Geometry
Chapter: Cross Sections, Solids of Rotation and Geometric Modeling
Common Core: G-GMD.B.4, G-MG.A.1, G-MG.A.2, G-MG.A.3
Time: 45 minutes
Total: 20 points (Question 1: 3 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 3 pts; Question 5: 2 pts; Question 6: 2 pts; Question 7: 3 pts; Question 8: 3 pts)

Geometry Modeling 3d Test: questions 1–5

Question 1: Name the cross sections (3 points)

Name the shape of each cross section.

Three solids and their cutting planes.

(1 point) The cut through the cylinder.
(1 point) The cut through the cone.
(1 point) The cut through the sphere.

Question 2: Cut through a cylinder (2 points)

A cylinder has a diameter of $12\text{ cm}$ and a height of $15\text{ cm}$. A plane passes through its axis perpendicular to the bases.

A cut through the axis.

(1 point) Name the shape of the cross section and give its dimensions.
(1 point) Find the area of the cross section.

Question 3: Slicing a sphere (2 points)

A sphere has a radius of $10\text{ cm}$. A plane cuts it $6\text{ cm}$ from the center.

A cut sphere, side view.

(1 point) Find the radius of the circular cross section.
(1 point) Find the area of the cross section in terms of $\pi$.

Question 4: Rotating a triangle (3 points)

A right triangle has legs of $5\text{ cm}$ and $12\text{ cm}$. It is rotated about the $12\text{ cm}$ leg.

Rotate the shape about the dashed axis.

(1 point) Name the solid.
(1 point) Give its radius and height.
(1 point) Find its volume in terms of $\pi$.

Question 5: Comparing counties (2 points)

County A has 31,200 residents on $40\text{ mi}^{2}$. County B has 24,640 residents on $28\text{ mi}^{2}$.

(1 point) Find the population density of each county.
(1 point) Which county is more densely populated, and by how many people per square mile?

Geometry Modeling 3d Test: questions 6–8

Question 6: Heating a gym (2 points)

A gym is $50\text{ ft}$ long, $30\text{ ft}$ wide and $12\text{ ft}$ tall. It needs 4 BTUs per cubic foot to be heated.

(1 point) How many BTUs are needed?
(1 point) A heater supplies $18{,}000$ BTUs per hour. How many hours does it take?

Question 7: Cheaper box (3 points)

Noah needs a box that holds $360\text{ in}^{3}$. Box 1 is $10\text{ in}$ by $6\text{ in}$ by $6\text{ in}$. Box 2 is $9\text{ in}$ by $8\text{ in}$ by $5\text{ in}$. Cardboard costs $\$0.03$ per square inch.

Two shipping boxes.