Answer
Verified
454.5k+ views
Hint: Here, first calculate the radius of the base as it circumference is given. Then apply the formula of volume of the right circular cylinder by assuming height h and equate that volume to the given volume of the cylinder. By solving the obtained equation we can get the value of the height of the cylinder.
Complete step by step answer:
Given, a right circular cylinder has a volume $81\pi .$
And the circumference of the base is $6\pi .$
Let r be the radius of the circular base and h be the height of the cylinder.
The base of the right circular cylinder is a circle in shape.
Given, the circumference of the circular base is $6\pi .$
[Circumference of circle = $2\pi r,$ where r is the radius of the circle]
$
\therefore 2\pi r = 6\pi \\
\Rightarrow r = \dfrac{{6\pi }}{{2\pi }} = 3 \\
$
Therefore, radius of right circular cylinder = 3 units
The volume of the cylinder with radius r and height h is given as $\pi {r^2}h$ .
$
\therefore \pi {r^2}h = 81\pi \\
\Rightarrow {(3)^2}h = \dfrac{{81\pi }}{\pi } = 81 \\
\Rightarrow h = \dfrac{{81}}{9} = 9 \\
$
Therefore, the height of the cylinder is 9 units.
Hence, (B) is correct.
Note:
In these types of questions, find the value of unknown things with the help of given value, by assuming radius and height as variable quantity. You must the formula of volumes and circumferences of basic shapes to solve these types of questions as these are directly based on a formula. Never put a formula containing more than one variable or you must have two equations for finding two variables. In this case, if you first apply the volume formula of the cylinder without finding the radius, it will be useless.
Alternatively, first, find the radius of the base, and then find the area of the base. Apply formula, Volume of cylinder = Area of circular base × Height, as the volume is given we can easily find the height of the cylinder by dividing the given area by area of the base.
Complete step by step answer:
Given, a right circular cylinder has a volume $81\pi .$
And the circumference of the base is $6\pi .$
Let r be the radius of the circular base and h be the height of the cylinder.
The base of the right circular cylinder is a circle in shape.
Given, the circumference of the circular base is $6\pi .$
[Circumference of circle = $2\pi r,$ where r is the radius of the circle]
$
\therefore 2\pi r = 6\pi \\
\Rightarrow r = \dfrac{{6\pi }}{{2\pi }} = 3 \\
$
Therefore, radius of right circular cylinder = 3 units
The volume of the cylinder with radius r and height h is given as $\pi {r^2}h$ .
$
\therefore \pi {r^2}h = 81\pi \\
\Rightarrow {(3)^2}h = \dfrac{{81\pi }}{\pi } = 81 \\
\Rightarrow h = \dfrac{{81}}{9} = 9 \\
$
Therefore, the height of the cylinder is 9 units.
Hence, (B) is correct.
Note:
In these types of questions, find the value of unknown things with the help of given value, by assuming radius and height as variable quantity. You must the formula of volumes and circumferences of basic shapes to solve these types of questions as these are directly based on a formula. Never put a formula containing more than one variable or you must have two equations for finding two variables. In this case, if you first apply the volume formula of the cylinder without finding the radius, it will be useless.
Alternatively, first, find the radius of the base, and then find the area of the base. Apply formula, Volume of cylinder = Area of circular base × Height, as the volume is given we can easily find the height of the cylinder by dividing the given area by area of the base.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Who was the Governor general of India at the time of class 11 social science CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Difference Between Plant Cell and Animal Cell