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Geometry and Measurement 6-8 / Week 03 / Thursday
4/6
Week 03 · Nets and Surface Area

Thursday

Counting the cardboard
// Unfold a box, add up its faces
⏱ about 20 min

Thursday: Counting the Cardboard

Rocket spreads the clubhouse plan on the Blueprint Table. "The walls are a box, 30 by 20 by 15 centimeters."

"And the roof is a pyramid with a 20 centimeter base and 15 centimeter triangles," Raven adds.

"We have sheets of cardboard, each 30 by 20," Rocket says. "How many do we need?"

"What do you notice about which faces we actually cut?" Raven asks.

Rocket thinks. "The floor is the table. No floor. The roof covers the top, so no top either. Four walls and four triangles."

Nova hovers above the plan, her light tracing each wall. "Then add," she says, "and divide by one sheet. Round up."

"Walls, fifteen hundred. Triangles, six hundred." Rocket divides. "Three and a half sheets. So four." Nova hums. "Four, and a scrap."

Faces the crew will cut

A box 30 cm long, 20 cm wide and 15 cm tall

The clubhouse walls are a box. The floor is the tabletop and the roof covers the top, so the crew cuts only the four walls.

Front and back: 30 × 15 = 450 each. The two ends: 20 × 15 = 300 each. Walls: 2 × 450 + 2 × 300 = 1,500.

The whole box, with top and bottom, would be 2,700 square centimeters. Leaving out two faces saves 1,200.

Raven's cardboard table

The crew's own clubhouse measurements and the cardboard each part needs, from Raven's Blueprint Book, in centimeters.

PartShapeEdges (cm)How manyCardboard (sq cm)
Front and back wallsrectangle30 by 152900
End wallsrectangle20 by 152600
Roof trianglestrianglebase 20, height 154600
Total to cut82,100

One roof triangle is ½ × 20 × 15 = 150. Four of them make 600. The roof's base is not cut: the box top is already there.

All the cardboard to cut: 1,500 + 600 = 2,100 square centimeters. One sheet is 30 × 20 = 600, so 2,100 ÷ 600 = 3.5. Round up: 4 sheets.

READ THE CARDBOARD TABLE
  • Read the question.
  • Tap your answer.
The clubhouse front wall is 30 by 15 cm. What is its area in square centimeters?
The clubhouse box is 30 by 20 by 15 cm. What is the area of its four walls, with no floor or top?
The roof pyramid has a 20 cm base and 15 cm triangles. What is the area of its four triangles?
The net of a box 30 by 20 by 15 cm: six rectangles laid flatIf the clubhouse box were closed on every side, 30 by 20 by 15 cm, what would its surface area be?
HOW MANY SHEETS?
  • Read the question.
  • Tap your answer.
The walls and roof need 2,100 square centimeters. One sheet is 600. How many whole sheets does the crew need?
The four walls alone need 1,500 square centimeters. One sheet is 600. How many whole sheets is that?
A small box needs 248 square centimeters. Scrap pieces are 100 square centimeters each. How many whole scraps?
What is the area of one end wall, in square centimeters? Type the number.
What is the total cardboard to cut for the walls and roof, in square centimeters? Type the number.
How many whole sheets of cardboard does the crew need? Type the number.
From the cardboard tableTrue or false?
The crew cuts cardboard for the floor of the clubhouse.?
2 × 450 + 2 × 300 = 1,500?
Three and a half sheets means the crew needs four whole sheets.?
The roof pyramid's square base is cut from cardboard too.?
WHY THIS EXERCISEA designer leaves out faces that are already covered, and rounds up because cardboard comes in whole sheets.
Try it
Design a model shed as a box with a pyramid roof. Choose three edges and a triangle height.
List the faces you would cut, find each area, add them, and work out the sheets you need.
Draw the net of the four clubhouse walls in a row, then the four roof triangles. Label every area.

Eight faces, four sheets. Tomorrow you find nets and surface area all around you and review the week.

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