A circular sheet of copper of radius 35 cm is at $20^{o} C$ . On heating, its area increases by $14.5 c m^{2}$ . If coefficient of linear expansion of copper is $1.7 \times 10^{- 5}^{o} C^{- 1}$ , find the temperature to which the sheet was heated.

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Solution

Radius of Sheet $= 35 c m$ at $20^{o} C$
$△ A = 14.5 c m^{2}$
Aerial Expansion is given by,
$△ A = A \times 2 \times α \times △ T (1) A = π \times {(35)}^{2} A = 3846.5 {c m}^{2} α = 1.7 \times 10^{- 5}$
So, putting values in equation $(1)$
$△ T = \frac{△ A}{A \times 2 α} = \frac{14.5}{3846.5 \times 2 \times 1.7 \times 10^{- 5}} △ T = 110.87 ℃ T = 110.87 + 20 ℃ T = 130.87 ℃$
It is heated to the above temperature.

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A circular sheet of copper of radius 35 cm is at 20oC. On heating, its area increases by 14.5cm2. If coefficient of linear expansion of copper is 1.7×10−5oC−1, find the temperature to which the sheet was heated.

Radius of Sheet =35cm at 20oC△A=14.5cm2Aerial Expansion is given by,△A=A×2×α×△T(1)A=π×(35)2A=3846.5cm2α=1.7×10−5So, putting values in equation (1)△T=△AA×2α=14.53846.5×2×1.7×10−5△T=110.87℃T=110.87+20℃T=130.87℃It is heated to the above temperature.

A circular sheet of copper of radius 35 cm is at $20^{o} C$ . On heating, its area increases by $14.5 c m^{2}$ . If coefficient of linear expansion of copper is $1.7 \times 10^{- 5}^{o} C^{- 1}$ , find the temperature to which the sheet was heated.