If the percentage change in length is 1- with change in temperature of a cuboid object -2-3- then what is percentage change in its area and volume-

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Standard XII

Mathematics

Average Rate of Change

If the percen...

Question

If the percentage change in length is $1 %$ with change in temperature of a cuboid object $(ℓ \times 2 ℓ \times 3 ℓ)$ then what is percentage change in its area and volume?

2 %, 6 %

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3 %, 6 %

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2 %, 3 %

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6 %, 9 %

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Solution

The correct option is C $2 %, 3 %$ .
The coefficient of linear expansion is $α$
The coefficient of Area expansion is $β = 2 α$
The coefficient of Volume expansion is $γ = 3 α$

The percentage in length is $Δ l / l \times 100 = α Δ T \times 100 = 1 %$
The percentage in Area is $Δ A / A \times 100 = β Δ T \times 100 = 2 α Δ T \times 100 = 2 \times 1 % = 2 %$
The percentage in Volume is $Δ V / V \times 100 = γ Δ T \times 100 = 3 α Δ T \times 100 = 3 \times 1 % = 3 %$

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If the percentage change in length is 1% with change in temperature of a cuboid object (ℓ×2ℓ×3ℓ) then what is percentage change in its area and volume?

If the percentage change in length is $1 %$ with change in temperature of a cuboid object $(ℓ \times 2 ℓ \times 3 ℓ)$ then what is percentage change in its area and volume?