Mass.gov
Massachusetts Department of Elementary and Secondary Education
Go to Selected Program Area
Massachusetts State Seal
Students & Families Educators & Administrators Teaching, Learning & Testing Data & Accountability Finance & Funding About the Department Education Board  
>
>
>
>
 
 
 
 
 
 
 
 
 
 
>
>
>
>
>
>
>

Massachusetts Comprehensive Assessment System

2017, Grade 10 Mathematics

Download PDF Document  Question 41: Open-Response calculator allowed
Three objects are shown below: a sphere, a right circular cylinder, and a right circular cone.

Three objects are shown: a sphere, a right circular cylinder, and a right circular cone.
The radius, r, of each of the objects is 10 inches.
  1. What is the volume, in cubic inches, of the sphere? Show or explain how you got your answer.
The height, h, of the cylinder is 2 times its radius.
  1. What is the volume, in cubic inches, of the cylinder? Show or explain how you got your answer.
The volume of the cone is equal to the volume of the cylinder.
  1. What is the value of k, the height in inches of the cone? Show or explain how you got your answer.
The radius of the sphere will be changed so that the volume of the sphere will be equal to the volume of the cylinder.
  1. By how many inches would the radius of the sphere have to change for its volume to be equal to the volume of the cylinder? 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.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Geometry concepts involved in using volume formulas for cylinders, cones, and spheres to solve problems. The student compares the volumes of three-dimensional objects.
4
3 The student response demonstrates a good understanding of the Geometry concepts involved in using volume formulas for cylinders, cones, and spheres 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 cylinders, cones, and spheres 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 cylinders, cones, and spheres to solve problems.
0 The student response contains insufficient evidence of an understanding of the Geometry concepts involved in using volume formulas for cylinders, cones, and spheres to solve problems to merit any points.

Note: There are 2 sample student responses for Score Point 4.

Grade 10 Mathematics

Question 17: Geometry
Question 20: Number and Quantity
Question 21: Statistics and Probability
Question 36: Algebra and Functions
Question 41: Geometry
Question 42: Algebra and Functions

Return to the MCAS 2017 Student Work Directory



Last Updated: March 1, 2017
E-mail this page| Print View| Print Pdf  
Massachusetts Department of Elementary and Secondary Education Search·Public Records Requests · A-Z Site Index · Policies · Site Info · Contact DESE