High School Geometry Practice - Measurement

CCSS Geometry Problems

 





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

QuestionCommon Core Standard #
1G.GMD.2 +
2G.GMD.3
3G.GMD.3
4G.GMD.3
5G.GMD.3
6G.GMD.3
7G.GMD.3
8G.GMD.4
9G.GMD.4
indicates a modeling standard.
+ indicates a college and career ready standard.

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



Question 1: The rectangular solid S and the prism P in the figure below have the same height. The base of S is a square with the sides of length a and the base of P is a right triangle with catheti of lengths a and 2a. If the volume of P is 200cm3, what is the volume of S?










Question 2: The standard ice hockey rink is rectangular with rounded corners, as shown in the figure below. Calculate the volume of ice from the rink, if the height of the ice is one tenth of a foot.









Question 3: An ice cream cone can be modeled by a semi sphere on top of a cone, as shown in the picture below. Calculate the volume of the ice cream cone as a function of r, if the height of the cone is h = 4r.









Questions 4 and 5: A sphere with a radius of 5cm is inscribed in a cylinder.


The ratio between the volume of the cylinder and the volume of the sphere is .

A cross-section by a horizontal plane at a height of 2 cm from the bottom of the cylinder intersects both solids. What is the area of the portion of the cross section inside the cylinder but outside the sphere?






Question 6: In the figure below, a sphere is inscribed in a right circular cone. What is the height of the cone if R = 4 inches and r = 2 inches?








Question 7: Given the triangle ABC in the figure below, sides AB and AC have the following lengths: AB = 3 and AC = 6. What is the volume of the shape formed by rotating the triangle around AB?









Question 8: The rectangle ABCD in the figure below has sides of lengths a and b. The volume of the shape formed by rotating the rectangle around AB is V1 and the volume of the shape formed by rotating the rectangle around BC is V2.
Calculate the ratio V1/V2.










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