Mission Payload: Volume of Shapes
Mission Payload: Packing a Deep Space Probe
Interactive Volume Worksheet | CCSS 8.G.C.9
In this engaging real-world math activity, students step into the role of spacecraft engineers tasked with preparing a deep space probe for launch. To succeed, they must calculate and compare the volumes of cylinders, cones, and spheres while working within realistic engineering constraints.
This worksheet moves beyond routine calculations and challenges students to apply volume formulas to meaningful decisions about capacity, efficiency, and optimization.
What Students Will Do
- Calculate the volume of a cylindrical fuel module used for surface operations
- Determine the minimum-size cylinder that meets fuel requirements
- Use the selected radius to calculate the volume of a cone-shaped sensor housing
- Choose the smallest cone that meets sensor space needs
- Compare multiple spherical communication beacons and select the largest one that fits within payload limits
- Track total volume using a payload meter and redesign when limits are exceeded
Key Math Concepts Covered
- Volume of a cylinder: V = πr²h
- Volume of a cone: V = (1/3)πr²h
- Volume of a sphere: V = (4/3)πr³
- Comparing volumes across different 3D shapes
- Understanding how radius and height affect volume
- Applying math to real-world engineering constraints
Why Teachers Love This Activity
- Fully aligned with Common Core Standard 8.G.C.9
- Interactive and auto-graded
- Focuses on reasoning and decision-making, not just computation
- Uses realistic numbers and constraints students can understand
- Encourages optimization by choosing the minimum size that works
- Supports randomization so each student gets different values
- Ideal for classwork, independent practice, or assessment
Grade Level and Use
- Best for Grade 8 Geometry
- Also suitable for STEM, engineering, or enrichment activities
- Can be completed in one class period or extended with discussion
Learning Objective
Students will use volume formulas for cylinders, cones, and spheres to evaluate design options, meet minimum capacity requirements, and optimize space within a fixed payload limit in an engineering scenario.
Randomization Available
This worksheet supports randomization. Each student receives different dimensions while working with the same mission constraints, which supports individual problem solving and prevents answer copying.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
