3D Solids Word Problems
Geometry Standards
HSG-GMD: Explain volume formulas and use them to solve problems
HSN-Q.A: Reason quantitatively and use units to solve problems
Approximately symbol ≈
Learning Intentions and Success Criteria
We are learning to:
- Sketch 3D solids and use volume formulas to solve real-world problems
- Solve real-world problems
Ms. Leon-Guerrero is throwing a party for her students whose birthday is this month. Each student chooses a pinata filled with candy. Emily's pinata is a cylinder solid. Tar's pinata is a square-based pyramid solid. De'Nya's pinata is a sphere solid. Elisa's pinata is a solid shaped like a pail. In the following questions, find how much candy did each student have in her pinata to share with her classmates.
For each problem, include correct units of measurement and round your answers to the nearest whole number or in terms of π.
1) Sketch and label Emily's cylinder pinata with a diameter of 25.7 centimeters and is 40.75 centimeters tall.
1) Calculate how much candy is in her pinata. Show your calculations.
2) Sketch and label Tar's pyramid pinata that has a square-base with an edge that measures 35 centimeters and is 50 centimeters tall.
2) Calculate how much candy is in her pinata. Show your calculations.
3) Sketch and label Elisa's pail shaped pinata that has a bottom base with a circumference of 26π centimeters, is 20 centimeters tall, and has the diameter of the top base that is twice the diameter of the bottom base.
3) Calculate how much candy is in her pinata. Show your calculations.
4) Draw and label De'Nya's sphere pinata has a diameter of 38 centimeters.
4) Her pinata is not full with candy because there is a teddy bear inside it. The teddy bear takes up one quarter of the volume of her pinata. Calculate how much candy is in her pinata. Show your calculations.
5) Which student's pinata has the most candy in it? Justify your answer and include your thinking.