QUESTION 4
Easy
Suppose the length of a rectangular box is 7 cm and breadth is 11cm. Find the volume if the height is i) 5cm, ii) 9cm, iii) 13cm. Find the linear pattern representing the volume of the rectangular box.
SOLUTION
1
Recall volume of rectangle formula
Volume = length × breadth × height
Given length \(= 7 cm\), breadth \(= 11 cm\)
So, Volume, \(V = 7 × 11 × height = 77 × height\)
Given length \(= 7 cm\), breadth \(= 11 cm\)
So, Volume, \(V = 7 × 11 × height = 77 × height\)
2
Calculate the volume for each height
i) height \(= 5 cm\)
\(V = 77 × 5 = 385 cm^3\)
ii) height \(= 9 cm\)
\(V = 77 × 9 = 693 cm^3\)
ii) height \(= 13 cm\)
\(V = 77 × 13 = 1001 cm^3\)
\(V = 77 × 5 = 385 cm^3\)
ii) height \(= 9 cm\)
\(V = 77 × 9 = 693 cm^3\)
ii) height \(= 13 cm\)
\(V = 77 × 13 = 1001 cm^3\)
3
Find the linear pattern
Let height \(= h\) cm. Then
\(V = 77h\)
This is a linear expression in \(h\).
\(V = 77h\)
This is a linear expression in \(h\).
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Final Answer :
Volume for each height: \((i)385, (ii)693, (iii)1001\)
Linear Expression: \(V = 77h\)
Concept Note
If base area is fixed(length × breadth = constant), then volume is linearly proportional to height.
\(V = base\) \(area × height\)