




Massachusetts Comprehensive Assessment System
2017, Grade 10 Mathematics
Question 41: 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: CCSS.Math.Content.HSGGMD.A.3  Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* 
Three objects are shown below: a sphere, a right circular cylinder, and a right circular cone.
The radius, r, of each of the objects is 10 inches.
 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.
 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.
 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.
 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.
Score  Description 
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 threedimensional 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: September 30, 2018


