Question

For given pair of quantity, check whether the first is proportional to the second. For proportional quantity, calculate the constant of proportionality.

The volume of water poured into a hollow prism and the height of the water level..

Accepted Answer

Given: The two quantities are

$(i)$ Volume of water poured

$(ii)$ Height of water level

Let volume be ' $v$ ' and the height of the water level from the base be ' $h$ '.

Let the base area of the prism be ' $a$ '.

The poured volume $=$ volume of the water column formed in the prism.

But volume of water column in the prism $=$ base area $\times$ height $= a h$

So we get $v = a h \Rightarrow h = \frac{v}{a}$

We can put whatever value we like for $v$ on the right side of the above equation. So $v$ is a variable. But $a$ is a constant for a prism.

Whatever value we give for $v$ , that value will be multiplied by a constant $\frac{1}{a}$ . So $h$ will always be proportional to $p$ .

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate. The constant of proportionality $k$ is given by $k = \frac{y}{x}$ where $y$ and $x$ are two quantities that are directly proportional to each other.

The constant of proportionality of "The volume of water poured into a hollow prism and the height of the water level" is $\frac{1}{a}$ .

Kerala Board Solutions for Chapter: Proportion, Exercise 2: Exercise 2

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Proportion, Exercise 2: Exercise 2

Questions from Kerala Board Solutions for Chapter: Proportion, Exercise 2: Exercise 2 with Hints & Solutions

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