Question

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating in the system.
A) $40073.98c{{m}^{2}}$
B) $300039.28c{{m}^{2}}$
C) $40009.28c{{m}^{2}}$
D) $44039.28c{{m}^{2}}$

Answer 1

Hint: The total radiating surface will be the total surface area of the cylindrical pipe. Use the formula “total surface area of a cylinder $=\left( 2\pi rh+2\pi {{r}^{2}} \right)$ “ to get the required area of radiating surface. Where r is the radius of the cylinder and ‘h’ is the height of the cylinder.
Complete step-by-step answer:

According to the question, there is a cylindrical pipe of length 28m and diameter 5cm in the water heating system. And we have to calculate the total radiating surface. The surface of the cylindrical pipe will be the radiating surface.
So, the total radiating surface will be the total surface area of this cylindrical pipe.
We know that,
Total surface area of a cylinder $=2\pi rh+2\pi {{r}^{2}}$ .
r = radius of the cylinder and
h= height of the cylinder = length of the cylinder.
For this cylindrical pipe
Height = length = 28 m = 2800cm
Diameter = 5 cm.
We know, radius $=\dfrac{diameter}{2}$ .
So, the radius of this cylindrical pipe $=\dfrac{5cm}{2}=2.5cm$ .
Now putting the value of height and radius in the above formula, we will get,
Total surface area of the cylindrical pipe $=2\pi \left( 2.5 \right)\left( 2800 \right)+2\pi {{\left( 2.5 \right)}^{2}}$ .
Taking $2\times \pi \times \left( 2.5 \right)$ common in RHS, we will get
\[\Rightarrow \] TSA of the cylindrical pipe $2\pi \left( 2.5 \right)\left( 2800+2.5 \right)$ .
$=\left( 2\pi \right)\left( 2.5 \right)\left( 2.802.5 \right)$
Taking $\pi =\dfrac{22}{7}$ , we will get,
TSA of the cylindrical pipe $=\dfrac{2\times 22 \times 2.5\times 2802.5}{7}$ .
$=44039.28c{{m}^{2}}$
Hence the required area of radiating surface $=44039.28c{{m}^{2}}$
Note: In question, length and diameter are given in different units. But in the formula of surface area, we need to use all the dimensions in the same unit. So be careful and first convert them into the same units.