Question 1
Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percentage. Provide an explanation and proof for your answer to receive full credit.
Question2
Ellis is painting wooden fenceposts before putting them in his yard. They are each 5 feet tall and have a diameter of 1 foot. There are 10 fenceposts in all. How much paint will Ellis need to paint all the surfaces of the 10 fenceposts? Use 3.14 for π, and round your answer to the nearest hundredth. Provide an explanation and proof for your answer to receive full credit.
Question 3
Use the chart below to answer the questions:
| Country | Population (1997 estimate) |
Area (square km) |
|---|---|---|
| Indonesia | 203,479,000 | 1,904,569 |
| Denmark | 5,248,000 | 42,077 |
| Ghana | 18,339,000 | 237,533 |
Which of these countries has the greatest population density? Which has the least? Provide an explanation and proof for your answer to receive full credit.
Question 4
A figure is located at (2, 0), (2, −2), and (6, 0) on a coordinate plane. What kind of 3-D shape would be created if the figure was rotated around the x-axis? Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation.
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