High School Geometry Practice - Modeling

CCSS Geometry Problems


This quiz is designed in accordance with the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school G.MG standards required for all students, including the college and career ready students.

Question 1: In the picture below, the distance between building A and river R is d = 1,200 yards. The river can be seen from a terrace of building A, situated at a height h = 24 yards from the ground. A builder plans to build a townhouse between building A and the river, at a distance of 300ft from building A. The goal of the builder is to increase the height of the townhouse as much as possible, without obstructing the river view from the terrace of building A. Which of the following is a better choice for the height of the townhouse?

Question 2: A balance beam has the cross section A in the figure below. The balance beam is made out of wood and its length is 500 cm. After the beam was manufactured, the designers realize that the longest edges of the beam are too sharp. The modified beam has the cross section B in the figure below. What is the volume of wood that was cut from the balance beam, if r = 1 cm?

Question 3: The cells of a beehive honeycomb are hexagonal and each hexagon is regular with sides of 0.4 cm. Estimate the number of cells that fit in a beehive with an area of 500 cm2.

Question 4: Approximate the Earth with a sphere with the radius of 6,371 km. What is the mass of the Earth if its average density is 5.52 g/cm3

Question 5: The state of Colorado can be approximated with a rectangle 380 miles long and 280 miles wide. What is the population density of Colorado if its population in 2013 is 5.188 million?

Question 6: The distance between New York and Los Angeles in a direct path along the Earth's surface is 2,400 miles. Assuming the Earth is a sphere with a radius of 4,000 miles, what is the angle between the radii in the figure below?

Question 7: A farmer buys 400 yards of fence for a new vegetable garden. If the shape of the garden is a rectangle, what is the maximum area that can be fenced with a 400 yards fence?

Question 8: A Christmas globe is made of plastic with a density of 2.2 g/cm3 and has a shape of a hollow sphere, as seen in the figure below. You measure the external diameter D = 8 cm of the globe and the weight w = 100 grams. What is the internal radius of the hollow sphere, r?

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