Question

An electrical geyser is cylindrical in shape, having a diameter of 35 cm and height 12m. Neglecting the thickness of its walls, calculate (i) Its outer lateral surface area (ii) Its capacity

Answer 1

Hint:
An electrical geyser is the electronic device which we use during winter for obtaining warm water for bath and other washing activities .Most probably you are familiar with this word. Every electrical geyser has some capacity to store water and which totally depends on the physical size and its shape. Here it is given that the shape of the geyser is cylindrical.it means right circular cylinder. For the right circular cylinder we have two parameters which determine its surface area, volume and base area etc. one is height and the other one is either radius or diameter. Here in question it is given that diameter is 35cm and geyser height is 12m.
It is noted that from the above data that all data are not in the same unit, first we convert all data in a single unit. Either in meters or centimeters. Let’s convert all data in meters. As we know that $1m=100cm$
Let’s move toward the outer lateral surface area which is sometimes known as curved surface area. Whose mathematical formula for calculating lateral surface area \[=2\pi rh\] and by the formula \[=\pi {{r}^{2}}h\], we can calculate volume.

Complete step by step solution:
Given: here in this question it is given that the shape of the electrical geyser is cylindrical and dimension of its diameter is 35cm,and height of geyser is 12m
It is given that the diameter of cylinder is 35cm and its height is 12 m
Now we have diameter in meter which is $\dfrac{35}{100}=0.35m$ and its radius is $\dfrac{0.35}{2}m$
Step 1: We know that for outer lateral surface area \[=2\pi rh\]
 \[\begin{align}
 & =2\pi \times \dfrac{32}{200}\times 12{{m}^{2}} \\
 & =12.0576\,\,{{m}^{2}} \\
\end{align}\]
Step 2: We know that the capacity means volume of the geyser which is equal to \[\pi {{r}^{2}}h\]
\[\begin{align}
 & =\pi \times {{\left( \dfrac{35}{200} \right)}^{2}}\times 12 \\
 & =1.15395\,\,{{m}^{3}} \\
\end{align}\]
Hence the outer lateral surface area is 12.0576 $m^2$ and capacity is 1.15395 $m^3$.

Note:
Students often confuse between lateral surface area and total surface area. Curved surface area and lateral surface area are the same. Other lateral surfaces may differ with inner lateral surface area if the thickness of the geyser material is significant compared to radius. let’s say if radius is 15cm and thickness is 2 cm then you can’t ignore it’s thickness. At that time it is essential to mention which lateral area we are talking about .