Find the lateral surface area and the total surface area of a cylinder with base radius 7 m and height 9 m.
$
A.{\text{ 396}}{m^2},704{m^2} \\
B.{\text{ 704}}{m^2},396{m^2} \\
C.{\text{ 396}}m,704m \\
D.{\text{ 704}}m,396m \\
$
Answer
362.1k+ views
Hint: Here we go through by applying the formula of lateral surface area of cylinder which is also known as curved surface area of cylinder i.e. $2\pi rh$. And for the total surface area we add the area of two circular faces to the lateral surface area.
Complete step-by-step answer:
Here in the question it is given that a cylinder with base radius 7 m and height 9 m.
Radius of cylinder, r=7 m.
And the height of the cylinder, h=9 m.
For finding the lateral surface area we apply the formula of lateral surface area i.e. $2\pi rh$
Lateral surface area = Area of the curved surface$ = 2\pi rh = 2 \times \dfrac{{22}}{7} \times 7m \times 9m = 396{m^2}$.
And for finding the total surface area we have to find the area of two circular surfaces and add with the lateral surface area.
We know that the area of the circle is $\pi {r^2}$.
$\therefore $Area of two circular curved surfaces$ = 2 \times \pi {r^2} = 2 \times \dfrac{{22}}{7} \times 7m \times 7m = 308{m^2}$.
Now the total surface area is the sum of lateral surface area and the two circular surfaces area. i.e. $396{m^2} + 308{m^2} = 704{m^2}$
Hence, option A is the correct answer.
Note: Whenever we face such a type of question the key concept for solving the question is calculate the area by simply applying the formula of lateral surface area and for total surface area we have to add the circular surface area to the curved surface area. We can figure it out by making a diagram of the cylinder to know about lateral surface and circular surface area.
Complete step-by-step answer:
Here in the question it is given that a cylinder with base radius 7 m and height 9 m.
Radius of cylinder, r=7 m.
And the height of the cylinder, h=9 m.
For finding the lateral surface area we apply the formula of lateral surface area i.e. $2\pi rh$
Lateral surface area = Area of the curved surface$ = 2\pi rh = 2 \times \dfrac{{22}}{7} \times 7m \times 9m = 396{m^2}$.
And for finding the total surface area we have to find the area of two circular surfaces and add with the lateral surface area.
We know that the area of the circle is $\pi {r^2}$.
$\therefore $Area of two circular curved surfaces$ = 2 \times \pi {r^2} = 2 \times \dfrac{{22}}{7} \times 7m \times 7m = 308{m^2}$.
Now the total surface area is the sum of lateral surface area and the two circular surfaces area. i.e. $396{m^2} + 308{m^2} = 704{m^2}$
Hence, option A is the correct answer.
Note: Whenever we face such a type of question the key concept for solving the question is calculate the area by simply applying the formula of lateral surface area and for total surface area we have to add the circular surface area to the curved surface area. We can figure it out by making a diagram of the cylinder to know about lateral surface and circular surface area.

Last updated date: 27th Sep 2023
•
Total views: 362.1k
•
Views today: 3.62k
Recently Updated Pages
What do you mean by public facilities

Difference between hardware and software

Disadvantages of Advertising

10 Advantages and Disadvantages of Plastic

What do you mean by Endemic Species

What is the Botanical Name of Dog , Cat , Turmeric , Mushroom , Palm

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Draw a welllabelled diagram of a plant cell class 11 biology CBSE

What is the nature of the Gaussian surface involved class 11 physics CBSE

Distinguish between Mitosis and Meiosis class 11 biology CBSE

Difference between physical and chemical change class 11 chemistry CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

Can anyone list 10 advantages and disadvantages of friction
