IM Geo.5.14 Lesson: Working with Pyramids
Here is a pyramid.
Which, if either, of these solids has the same volume as the pyramid?
Calculate the volume of each solid. Round your answers to the nearest tenth if necessary.
height 12 cm; area of base 32 cm²
A particular cone has radius r and height h.
Write an expression for the volume of this cone in terms of and .
What is the height of a cone whose volume is cubic units and whose radius is 3 units?
What is the radius of a cone whose volume is cubic units and whose height is 3 units?
The Pyramid of Giza is 455 feet tall. The base is square with a 756-foot side length. How many Olympic-size swimming pool volumes of water can fit inside the Pyramid of Giza? Explain or show your reasoning.
A caterer is making an ice sculpture in the shape of a pyramid for a party. The caterer wants to use 12 liters of water, which is about 720 cubic inches. The sculpture must be 15 inches tall. The caterer needs to decide how large to make the base, which can be any shape.
- Draw and label the dimensions of a base that would work.
- Find a second base that satisfies the baker’s requirements. You may use the applet to help, if you choose.
Directions for using the applet:
- Draw your base on the grid with the Polygon tool.
- Change to the 3D Graphics View by clicking on button.
- Click in the 3D window to switch back to the 3D menu.
- Select the Extrude to Pyramid tool and click on your polygon.
- When the dialog box opens, input the height.
- Use the Volume tool to verify your calculations and your figure.
- Refresh the page and repeat the steps with another base that works.