Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 4

4 / 5

Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if the height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm.

Find the linear pattern representing the volume of the rectangular box.

Answer

1
Use the volume formula for a rectangular box and substitute each given height.
\text{Volume = length × breadth × height = ${color:#2E2EFF}7{/color}$ × ${color:#2E2EFF}11{/color}$ × height = 77 × height}
\text{(i) 77 × ${color:#2E2EFF}5{/color}$ = 385 cm^3 $\quad$ ${color:#625b5f}[height = 5 cm]{/color}$}
\text{(ii) 77 × ${color:#2E2EFF}9{/color}$ = 693 cm^3 $\quad$ ${color:#625b5f}[height = 9 cm]{/color}$}
\text{(iii) 77 × ${color:#2E2EFF}13{/color}$ = 1001 cm^3 $\quad$ ${color:#625b5f}[height = 13 cm]{/color}$}
2
Write the volumes in the given order.
Answer: The volumes are 385 cm^3, 693 cm^3, and 1001 cm^3.
3
Compare consecutive volumes to find the common difference.
\text{693 - 385 = 308 cm^3 $\quad$ ${color:#625b5f}[height changes from 5 cm to 9 cm]{/color}$}
\text{1001 - 693 = 308 cm^3 $\quad$ ${color:#625b5f}[height changes from 9 cm to 13 cm]{/color}$}
Therefore, the common difference is 308 cm^3.
4
Write the linear pattern for the volume.
Answer: The linear pattern is 385, 693, 1001,…, with a common difference of 308 cm^3.
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