Question

What is $113^\circ F$ in Celsius?
A. $35^\circ C$
B. $45^\circ C$
C. $55^\circ C$
D. $65^\circ C$

Answer 1

Hint: $^\circ C,^\circ F$ are both the temperature scales and here $^\circ c$ represent the temperature in degree Celsius and $^\circ F$ represent the temperature in degree Fahrenheit
Hence we can use the formula
$T(^\circ F) = T(^\circ C)\left( {\dfrac{9}{5}} \right) + 32$
Here $T(^\circ C)$ is the temperature in Celsius
$T(^\circ F)$ is the temperature in Fahrenheit.

Complete step-by-step answer:
As we know that the temperature is the degree or intensity of the heat present in any object or body which can be shown using the thermometer. In thermometer we can measure the temperature in the two scales on in the $^\circ C$ and other is the $^\circ F$
As temperature is the physical quantity and kelvin is the SI unit of the temperature and there is the relation between the kelvin and the $^\circ C$ scale that $T(^\circ C) = T(K) - 273$
Here $T(^\circ C)$ is the temperature in Celsius
And $T(K)$ is the temperature in Kelvin
And we should know that zero kelvin is considered as the absolute zero temperature
Now here we need to find the relation between the \[^\circ C,^\circ F\]
Here we know that the freezing point of the water is $32^\circ F$ and its boiling point is $212^\circ F$
So the difference between the freezing and the boiling point is equal to $ = 212^\circ F - 32^\circ F$$ = 180^\circ F$
Now in the Celsius scale we know that
Freezing point of water$ = 0^\circ C$
Boiling point of water$ = 100^\circ C$
So the difference would be $ = 100^\circ C - 0^\circ C$$ = 100^\circ C$
Now the ratio of their difference$ = \dfrac{{100}}{{180}} = \dfrac{5}{9}$
And we know that $32^\circ F$ is equivalent to $0^\circ C$
So the formula to change $^\circ C$ to $^\circ F$ would become
$T(^\circ F) = T(^\circ C)\left( {\dfrac{9}{5}} \right) + 32$
Or we can write it as
$T(^\circ C) = (T(^\circ F) - 32)\dfrac{5}{9}$
So here in this question we are given the temperature as $113^\circ F$
So putting it in the above equation we get that
$T(^\circ C) = (113 - 32)\dfrac{5}{9} = (81)\dfrac{5}{9} = 45^\circ C$
Hence we can say that $113^\circ F = 45^\circ C$
Hence option B is correct.

Note: The normal body temperature of the human body is $37^\circ C$ and in Fahrenheit it is $98.6^\circ F$ and the thermometer we use to get the reading is $^\circ F$ scale thermometer.