Question

The inner diameter of a circular well is 3.5 m. it is 10 m. deep, find its inner curved surface area.

Answer 1

Hint: To solve this we need to know the formula for inner curved surface area \[2 \pi rh \] . Where \[r \] is an inner radius of the circular well. \[h \] is the depth of a circular well. Also know that diameter is half of the radius. Since we have diameter we convert it into radius. Substituting the values in the given formula we obtain the surface area.

Complete step-by-step answer:
Given, diameter and depth. That is \[d = 3.5\;m \] and \[h = 10\;m \] .
If we represent the given word problem in diagram we get,

Inner radius \[r \] can be found by dividing the diameter by 2.
  \[ r = \dfrac{d}{2} \] Where \[d = 3.5\;m \] . Substituting we get,
  \[ r = \left( { \dfrac{{3.5}}{2}} \right)\;m \]
  \[ r = 1.75\;m \]
We know \[r = 1.75m \] and \[h = 10\;m \] , both the units are in S.I. units.
So, substituting in inner surface area \[ = 2 \pi rh \]
  \[ = 2 \times \dfrac{{22}}{7} \times 1.75 \times 10 \] (We know \[ \pi = \dfrac{{22}}{7} \] )
  \[ = 2 \times \dfrac{{22}}{7} \times 17.5 \]
  \[ = 2 \times \dfrac{{22}}{7} \times 17.5 \]
  \[ = \dfrac{{770}}{7} \]
  \[ = 110\;{m^2} \]
That is, the inner diameter of a circular well is 3.5 m. it is 10 m. deep, has an inner curved surface area of \[110\;{m^2} \] . (Area is always in meter square.)
So, the correct answer is “110 sq.m”.

Note: By plotting the diagram it will give some idea of what needs to be calculated. While doing the problems always check the units of radius and height which are in S.I. unit. If not convert into S.I. unit and solve. If the given radius or depth are not in S.I. units then you will get the wrong answer. Always remember the formula of surface area of cylinder, surface area of triangle etc. So that you can solve any problem in finding the surface area.