Which of the following options has pairs of quantities where the first quantity is directly proportional to the second one?

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

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Length and breadth of rectangle

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Area and radius of cirlces

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Perimeter and radius of circles

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Solution

The correct options are
A
The volume of water poured into a hollow prism and height of the water level.

C
Area and radius of cirlces

D
Perimeter and radius of circles

$C i r c u m f e r e n c e o f a c i r c l e = 2 π \times R a d i u s o f C i r c l e$ .

Hence, $C i r c u m f e r e n c e \propto R a d i u s$

$A r e a o f a c i r c l e = π r^{2}$ and thus $A r e a \propto S q u a r e o f R a d i u s$
$⟹ A r e a \propto R a d i u s$

Area of rectangle = length x breadth (length is inversely proportional to breadth, area being constant)

$V o l u m e = B a s e a r e a \times H e i g h t$ and hence, $V o l u m e \propto H e i g h t$

i.e., The volume of water poured into a hollow prism and height of the water level are in direct proportion.

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