Question

If the length of a cylinder on heating increases by 2%, the area of its base will increase by ______.

Options

• 0.5%

• 2%

• 1%

• 4%

Answer 1

If the length of a cylinder on heating increases by 2%, the area of its base will increase by 4%.

Explanation:

Assuming the initial length of the cylinder is ℓ₁, the linear expansion coefficient is α, and the temperature rise is Δt°C,

Δℓ = ℓ αΔt  ⇒ `(Deltaℓ)/ℓxx100` = αΔt × 100

∴ 2 = αΔt × 100

Now, for area

ΔA = AβΔt ⇒ `(Delta"A")/"A"` = βΔt

⇒ `(Delta"A")/"A"xx100` =  βΔt × 100

% change in area = βΔt  × 100

= βΔt × 100

We know that 2 × α × Δt = β × Δt

= 2αΔt × 100

= 2(αΔt × 100)

= 2 × 2

= 4%