Page 62 - Mathematics Class - XII

ACTIVITY 4.4

OBJECTIVE
To construct an open box of maximum volume from a given rectangular sheet by cutting equal squares from
each corner.

MATERIAL REQUIRED

Y White chart papers Y Calculator
Y Pair of scissors Y Geometry box
Y Cellotape / Glue stick

PRE-REQUISITE KNOWLEDGE
1. Knowledge of basic paper folding.
2. Knowledge of formulae of volume and area of solid figures.

PROCEDURE
1. Take a rectangular chart paper of size 25 cm × 15 cm and name it as PQRS.
2. Cut four equal squares each of side x cm from each corner P, Q, R and S.

3. Repeat the process by taking the same size of chart paper and different value of x.
4. Make an open box by folding the flaps of the sheet using cellotape/adhesive.

S x x R
x x

15 cm

x x
P x x Q
25 cm

Fig. (a)

DEMONSTRATION

1. When x = 1, volume of the box = (25 – 2) × (15 – 2) × 1 cm = 299 cm 3
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2. When x = 2, volume of the box = (25 – 4) × (15 – 4) × 2 cm = 462 cm 3
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3. When x = 3, volume of the box = (25 – 6) × (15 – 6) × 3 cm = 513 cm 3
3
4. When x = 4, volume of the box = (25 – 8) × (15 – 8) × 4 cm = 476 cm 3
3
5. When x = 5, volume of the box = (25 – 10) × (15 – 10) × 5 cm = 375 cm 3
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6. When x = 6, volume of the box = (25 – 12) × (15 – 12) × 6 cm = 234 cm 3
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Here, we see that volume of the box is maximum when x = 3.

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