Question 4

We will use the formula for the volume of a rectangular box.

Step 1 — Find the base area

Let's first find the base area. The length of the box is 7 cm. The breadth of the box is 11 cm. The formula for base area is length times breadth.

$\text{Base Area} = \text{Length} \times \text{Breadth}$

$= 7 \times 11$

$\boxed{77 \text{ cm}^2}$

Step 2 — Calculate volumes for different heights

Now we can find the volume for each given height. The volume formula is base area times height.

(i) Height is 5 cm.

$\text{Volume} = 77 \times 5$

$\boxed{385 \text{ cm}^3}$

(ii) Height is 9 cm.

$\text{Volume} = 77 \times 9$

$\boxed{693 \text{ cm}^3}$

(iii) Height is 13 cm.

$\text{Volume} = 77 \times 13$

$\boxed{1001 \text{ cm}^3}$

Step 3 — Determine the linear pattern

Let's find a general pattern for the volume. Let the height of the box be $h$ cm. We know the base area is 77 cm². The volume $V$ is base area multiplied by height.

$V = 77 \times h$

$\boxed{V = 77h}$

Answer

(i) The volume is 385 cm³. (ii) The volume is 693 cm³. (iii) The volume is 1001 cm³. The linear pattern is V = 77h.