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Geometry: Unit 7

Last updated 9 months ago
14 questions
Unit 7 - Item 1

1

Part A
Use trigonometric ratios to find the height and radius of the cone rounded to the nearest tenth. Determine the volume of the cone including the base rounded to the nearest centimeter.

1

Part B
Assuming the cones are stackable, how many cones could be placed under a shelf that measures 30 𝑙𝑒𝑛𝑔𝑡ℎ, 70 𝑤𝑖𝑑𝑡ℎ, 𝑎𝑛𝑑 50 ℎ𝑒𝑖𝑔ℎ𝑡?

Unit 7 - Item 2
The following image shows a mailbox that sits on top of a decorative stand.
1

Part A
Select the geometric components of the mailbox including the post.

1

Part B
Write an expression to find the total volume of the mailbox including the portion of the square post. Calculate the total volume rounded to the nearest inch?

Unit 7 - Item 3
Javon, a senior, of a local high school basketball team has just scored his 1,000th point. His
coach presented him an official Georgia High School Association (GHSA) basketball after the
game to recognize his accomplishment. The basketball has a volume of 435 cubic inches.

1

Part A
If the basketball has a volume of 435 cubic inches, what is the radius of the basketball rounded to the nearest tenth? Use 3.14 for π.

1

Part B
Javon’s coach had a cubic box made that has a volume of 729 in³. Explain if the cubic box will be able to store Javon’s GHSA basketball.

1

Part C
Javon’s sister, Bre, also plays basketball. The circumference of her basketball is 28.5 inches. Compare by finding the difference in volume of both Javon’s and Bre’s basketball. Use 3.14 for
π. Round your answer to the nearest tenth.

1

Part D
Suppose Javon wanted to store his basketball in a cylindrical container rather than a cubic box.
If the cylindrical container has a radius of 5 inches and a height of 9.5 inches, what portion of the box that is empty? Use 3.14 for π. Round the answer to the nearest hundredth.

Unit 7 - Item 4
One of the most recognizable structures in Las Vegas is the Luxor Hotel and Casino, a 30-story pyramid.


Fun Facts:
  • It is the 3rd largest hotel in Las Vegas and the 6th largest in the world.
  • At 350 ft high, it is also the tallest pyramid in the US, and the 4th tallest in the world.
  • Each side of the square base measures 646 feet long.
  • The resort contains the world's largest lobby by volume, measuring 29 million cubic feet.
  • The top of the pyramid features a light beam, which shines up into the sky and is the most powerful man-made light in the world.

1

Part A
What is the volume of the resort without the lobby?

1

Part B
The following three students begin to calculate the distance from the base corner of the pyramid
to exact center of the ground floor, directly under the center beam light. Explain how each equation would lead to the correct answer, then continue to find the distance from the corner of
the pyramid to under the center beam of light.

Student 1:

Student 2:

Student 3:

Unit 7 - Item 5
Design three different popcorn containers using geometric shapes such as a cylinder, cone, and rectangular prism (box).
  1. Sketch each container with labeled dimensions for the radius, height, length and width.
  2. Calculate the volumes for each container.
  3. Comparing the volume for each of the containers. Determine which container has the largest volume (can hold the most popcorn).
  4. Determine a fair selling price for each of the containers.
  5. Create a menu (e.g., PowerPoint, Google Slides) showcasing the designed popcorn containers, their dimensions, volume calculations, and comparisons.
  6. Discuss findings and conclusions based on the volume comparisons.
  7. Explain how polynomial equations were used to calculate volumes and facilitate the comparison
1

Complete steps 1-7.

Rubric:

Unit 7 - Item 6
The data table below shows the mass and volume of three samples of the same mineral.
1

Part A
Calculate the density for each sample given the formula
where ρ (rho) represents density
𝑚 represents mass, and 𝑉 represents volume.

1

Explain which student, Melody or Alfred, correctly modeled the relationship between the density and volume from each of the samples.

Unit 7 - Item 7
1

Jordan needs to stack these cones under a table that is 4 feet tall.
How many cones can he stack on top of each other, and they still fit under the table?