




Massachusetts Comprehensive Assessment System
2016, Grade 10 Mathematics
Question 42: OpenResponse 

Reporting Category: Geometry Standard: 10.M.2  Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area. Standard: Mathematics.G.GMD.1.03  Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* 
A wooden cube with an edge length of 3 inches is composed of six congruent right square pyramids. The cube and one of the pyramids is shown in the diagram below.  What is the volume, in cubic inches, of the entire cube? Show or explain how you got your answer.
 What is the volume, in cubic inches, of one of the six pyramids? Show or explain how you got your answer.
 What is the total surface area, in square inches, of the cube? Show or explain how you got your answer.
 What is the total surface area, to the nearest square inch, of one of the six pyramids? Show or explain how you got your answer.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Geometry concepts involved in using volume formulas for pyramids to solve problems. The student finds the surface area and volume of a right square pyramid which is a part of the composition of a cube. 
4 
3 
The student response demonstrates a good understanding of the Geometry concepts involved in using volume formulas for pyramids to solve problems. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points. 
2 
The student response demonstrates a fair understanding of the Geometry concepts involved in using volume formulas for pyramids to solve problems. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates a minimal understanding of the Geometry concepts involved in using volume formulas for pyramids to solve problems. 
0 
The student response contains insufficient evidence of an understanding of the Geometry concepts involved in using volume formulas for pyramids to solve problems to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Algebra and Functions
 Question 20: Geometry
 Question 21: Number and Quantity
 Question 36: Algebra and Functions
 Question 41: Statistics and Probability
 Question 42: Geometry
Return to the MCAS 2016 Student Work Directory
Last Updated: April 5, 2018


