
The outer and inner diameters of a circular pipe are 6 cm and 4 cm respectively. If its length is 10 cm then what is the total surface area in square centimeters?
A. \[55\pi \]
B. \[110\pi \]
C. \[150\pi \]
D. None of the above
Answer
444.6k+ views
Hint: Here we need to find the total surface area of a pipe. We know that the pipe is in the shape of a hollow cylinder. So we will use the formula of area of a hollow cylinder to calculate the area of a pipe. We will substitute the value of the outer radius, inner radius and the length in the formula of the hollow cylinder to get the find value of the total surface area of the pipe.
Complete step by step solution:
Here we need to find the total surface area of a pipe. The given pipe is in the shape of a hollow cylinder.
It is given that the outer diameter of a pipe is 6 cm and the inner diameter of a circular pipe is 4 cm.
Now, we will draw the figure using the given information.
We know that the formula for the area of a hollow cylinder is given by
$Area = 2\pi h\left( {{r_2} + {r_1}} \right) + 2\pi \left( {{r_2}^2 - {r_1}^2} \right)$
${r_2} = \dfrac{6}{2}cm = 3cm$ , ${r_1} = \dfrac{4}{2}cm = 2cm$ and $h = 10cm$
Now, we will substitute the value of outer radius, inner radius and the length of a pipe in the formula.
$ \Rightarrow Area = 2 \cdot \pi \cdot 10 \cdot \left( {3 + 2} \right) + 2 \cdot \pi \cdot \left( {{3^2} - {2^2}} \right)$
On simplifying the terms, we get
$ \Rightarrow Area = 2 \cdot \pi \cdot 10 \cdot 5 + 2 \cdot \pi \cdot 5$
On multiplying the terms, we get
$ \Rightarrow Area = 100\pi + 10\pi $
On adding the terms, we get
$ \Rightarrow Area = 110\pi c{m^2}$
Hence, the total surface area of a pipe is equal to $110\pi c{m^2}$.
Hence, the correct answer is option B.
Note:
Remember that the total surface area of a hollow cylinder is equal to lateral surface area and the area of the solid bases. To find the total surface area of a hollow cylinder, we need both outer and inner radii of the hollow cylinder and the length of the hollow cylinder.
Complete step by step solution:
Here we need to find the total surface area of a pipe. The given pipe is in the shape of a hollow cylinder.
It is given that the outer diameter of a pipe is 6 cm and the inner diameter of a circular pipe is 4 cm.
Now, we will draw the figure using the given information.

We know that the formula for the area of a hollow cylinder is given by
$Area = 2\pi h\left( {{r_2} + {r_1}} \right) + 2\pi \left( {{r_2}^2 - {r_1}^2} \right)$
${r_2} = \dfrac{6}{2}cm = 3cm$ , ${r_1} = \dfrac{4}{2}cm = 2cm$ and $h = 10cm$
Now, we will substitute the value of outer radius, inner radius and the length of a pipe in the formula.
$ \Rightarrow Area = 2 \cdot \pi \cdot 10 \cdot \left( {3 + 2} \right) + 2 \cdot \pi \cdot \left( {{3^2} - {2^2}} \right)$
On simplifying the terms, we get
$ \Rightarrow Area = 2 \cdot \pi \cdot 10 \cdot 5 + 2 \cdot \pi \cdot 5$
On multiplying the terms, we get
$ \Rightarrow Area = 100\pi + 10\pi $
On adding the terms, we get
$ \Rightarrow Area = 110\pi c{m^2}$
Hence, the total surface area of a pipe is equal to $110\pi c{m^2}$.
Hence, the correct answer is option B.
Note:
Remember that the total surface area of a hollow cylinder is equal to lateral surface area and the area of the solid bases. To find the total surface area of a hollow cylinder, we need both outer and inner radii of the hollow cylinder and the length of the hollow cylinder.
Recently Updated Pages
The orthocenter of a rightangled triangle is formed class 10 maths CBSE

A lending library has a fixed charge for the first class 10 maths CBSE

A ladder is placed along a wall of a house such that class 10 maths CBSE

The given figure is the symbol for which component class 10 physics CBSE

Choose the correct meaning of the idiomphrase Oily class 10 english CBSE

Write the laws of refraction of light Explain the same class 10 physics CBSE

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What constitutes the central nervous system How are class 10 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE
