Week 11 · Volume: Where the Formulas Come From
Shop Day
Shop Day: three containers
// Paint, foam and a jug of water
⏱ about 20 min
Shop Day: Three Containers
Comet lines up a mug, a cereal box and a ball on the kitchen table. "Shop Day. Three shapes, three volumes."
"Measure first, compute second, check third," Wren says. "What do you notice about the mug?"
"A cylinder, if you ignore the handle. Radius 4, height 10." She writes it down.
Nova projects a measuring cup beside the mug. "Would you like a hint? Count cups to check the order, not the exact number."
"Box, then mug, then ball," Comet predicts. The cups agree.
"Our designer," Wren says, "run this with your family. Predict the order before you pour."
- A circle's area is πr² (the wedge row), and a cylinder's volume is πr²h (stacked discs).
- A pyramid is Bh/3 and a cone is πr²h/3: three fill the matching prism or cylinder.
- A sphere is 4/3 πr³. Scaling every length by k multiplies the volume by k³.
- A slice leaves a cross-section. A spin sweeps a flat shape into a solid.
◇ MODEL, MEASURE, CHECK
Together, pick three containers: something round like a mug, a box, and a ball or a bowl.
Name the solid each one is closest to. Measure the lengths you need with a ruler.
Compute each volume with the formula. Use 3.14 for π. Predict which holds the most.
Check with water or dry rice over a tray: count cups into the mug and the box. Does the order match?
Name the solid each one is closest to. Measure the lengths you need with a ruler.
Compute each volume with the formula. Use 3.14 for π. Predict which holds the most.
Check with water or dry rice over a tray: count cups into the mug and the box. Does the order match?
For a grown-up
Keep the water or rice over a tray and wipe spills at once. The student does the measuring and the formulas.
Ask which formula they used for each container and why the mug counted as a cylinder.
A ball cannot be filled, so compare it by the formula only, or press it into a bowl of rice.
Ask which formula they used for each container and why the mug counted as a cylinder.
A ball cannot be filled, so compare it by the formula only, or press it into a bowl of rice.
SHOP DAY CHECK
- Read the question.
- Tap your answer.
A mug is a cylinder with radius 4 cm and height 12 cm. What is its volume in cubic centimeters? Use 3.14 for π.A cereal box is 20 by 8 by 30 cm. What is its volume in cubic centimeters?
A ball has radius 6 cm. What is its volume in cubic centimeters? Use 3.14 for π.A cereal box is 20 by 8 by 30 cm. What is its volume in cubic centimeters? Type the number.
Multiply the three edge lengths.
WHY THIS EXERCISEA box is the simplest prism: base area 20 × 8, then times the height 30.
Draw your three containers with their measurements and the formula beside each.
Week eleven complete, designer. Next week every prop becomes a shape on paper, and the set opens.