narrative report
Solving Problems Involving
Prisms and Cylinders
Focus on…
After this lesson, you will be able to… solve problems involving right rectangular prisms, right triangular prisms, and right cylinders Danielle works at a toy store that sells remote control cars. She wants to fit 60 car boxes into a large crate. The car boxes have dimensions of
50 cm × 30 cm × 20 cm. The crate has dimensions of 140 cm × 120 cm
× 110 cm. Predict whether all 60 boxes fit in the crate.
How can you solve a problem involving volume?
• centimetre cubes
• centimetre grid paper
Estimate the number of boxes that could fit into the crate.
3.
MHR • Chapter 7
Calculate the volume of one car box and the volume of the crate described above.
2.
268
1.
Model the problem.
a) On centimetre grid paper, draw a rectangle to model the bottom of the crate. What measurements did you use?
b) Using centimetre cubes, make a model of the car box. How did you arrange the cubes?
c) Inside the rectangle you drew on grid paper, trace around your model of the box repeatedly to show how you could place the boxes on the bottom row in the crate. How many boxes did you draw?
How many layers of boxes will fill the crate?
e) How many boxes will you fit into the crate altogether?
d)
Compare your answers to #3 with those of your classmates.
What was the greatest number of boxes that fit into the crate?
b) Could you arrange your boxes differently to improve the modelled number of boxes that would fit in the crate? Explain.
4. a)
Reflect on Your Findings
5.
How did the estimated number of boxes compare with the modelled number of boxes that would fit in the crate? Explain any differences.
Example 1: Solve a Problem Involving Right Triangular Prisms
Marcus is making a display of packages of Prism Chocolates in his candy shop. He will stack 64 packages to form a shape that is a triangular prism, using eight packages in the bottom layer. What is the volume
Prisms and Cylinders
Focus on…
After this lesson, you will be able to… solve problems involving right rectangular prisms, right triangular prisms, and right cylinders Danielle works at a toy store that sells remote control cars. She wants to fit 60 car boxes into a large crate. The car boxes have dimensions of
50 cm × 30 cm × 20 cm. The crate has dimensions of 140 cm × 120 cm
× 110 cm. Predict whether all 60 boxes fit in the crate.
How can you solve a problem involving volume?
• centimetre cubes
• centimetre grid paper
Estimate the number of boxes that could fit into the crate.
3.
MHR • Chapter 7
Calculate the volume of one car box and the volume of the crate described above.
2.
268
1.
Model the problem.
a) On centimetre grid paper, draw a rectangle to model the bottom of the crate. What measurements did you use?
b) Using centimetre cubes, make a model of the car box. How did you arrange the cubes?
c) Inside the rectangle you drew on grid paper, trace around your model of the box repeatedly to show how you could place the boxes on the bottom row in the crate. How many boxes did you draw?
How many layers of boxes will fill the crate?
e) How many boxes will you fit into the crate altogether?
d)
Compare your answers to #3 with those of your classmates.
What was the greatest number of boxes that fit into the crate?
b) Could you arrange your boxes differently to improve the modelled number of boxes that would fit in the crate? Explain.
4. a)
Reflect on Your Findings
5.
How did the estimated number of boxes compare with the modelled number of boxes that would fit in the crate? Explain any differences.
Example 1: Solve a Problem Involving Right Triangular Prisms
Marcus is making a display of packages of Prism Chocolates in his candy shop. He will stack 64 packages to form a shape that is a triangular prism, using eight packages in the bottom layer. What is the volume