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# MAFS.8.G.3.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Subject Area: Mathematics
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. (Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### Remarks/Examples

Fluency Expectations or Examples of Culminating Standards

When students learn to solve problems involving volumes of cones, cylinders, and spheres — together with their previous grade 7 work in angle measure, area, surface area and volume (7.G.2.4–2.6) — they will have acquired a well-developed set of geometric measurement skills. These skills, along with proportional reasoning (7.RP) and multistep numerical problem solving (7.EE.2.3), can be combined and used in flexible ways as part of modeling during high school — not to mention after high school for college and careers.

### TEST ITEM SPECIFICATIONS

• Item Type(s): This benchmark may be assessed using: EE item(s)

• Assessment Limits :
Graphics of three-dimensional figures can be included. Dimensions must be given as rational numbers. Figures must not be composite
• Calculator :

Yes

• Context :

Allowable

### SAMPLE TEST ITEMS (4)

• Test Item #: Sample Item 1
• Question:

A cylinder with a height of  inches (in.) and a diameter of 5 inches is shown.

What is the volume of the cylinder, in cubic inches? (Use 3.14 for )

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 2
• Question:

The diameter of a sphere is 4 inches.

What is the volume of the sphere, in cubic inches? (Use 3.14 for ??.)

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 3
• Question:

A cone has a height of 6.4 inches and a diameter of 6 inches.

What is the volume, in cubic inches, of the cone? Use 3.14 for

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 4
• Question:

A water container in the shape of a cone has a height of 5 inches and a diameter of 3.5 inches.

Enter an equation in the first blank box and a number in the second blank box to complete the statements about the water container.

A. The formula to calculate the container's volume, V, with the given measurements is ________.

B. The container can hold approximately _____ cubic inches of water. Round your answer to the nearest hundredth.

• Difficulty: N/A
• Type: EE: Equation Editor