Answer
Verified
480k+ views
Hint: The largest circular cone that can be cut out of the cube will have height equal to cube edge and base diameter of cone will be equal to edge of the cube.
Largest right circular cone will have the same height. Let this height be h.
Diameter of the base of the cone is equal to the edge of the cube since it touches all the edges of the cube side.
Let the radius be r.
$ \Rightarrow h = 9cm\;\& \;r = \dfrac{{diameter}}{2} = \dfrac{9}{2} = 4.5cm$
We know that volume of a cone with radius r and height h is
Volume $ = \dfrac{1}{3}\pi {r^2}h$
Substituting r and h values in the above formula, we get
$ \Rightarrow Volume = \dfrac{1}{3}\pi {\left( {4.5} \right)^2}9 = 190.85c{m^3}$
$\therefore $ The volume of the largest right circular cone formed from the given cube is $190.85c{m^3}$
Note:
Here the base of the cone will be the circle inscribed in the face of the cube and its height will be equal to the edge length of the cube. We need to visualize the given problem in geometrical structures to solve the problem easily. When we represent the given problem in graphical form it looks similar to the below figure.
Largest right circular cone will have the same height. Let this height be h.
Diameter of the base of the cone is equal to the edge of the cube since it touches all the edges of the cube side.
Let the radius be r.
$ \Rightarrow h = 9cm\;\& \;r = \dfrac{{diameter}}{2} = \dfrac{9}{2} = 4.5cm$
We know that volume of a cone with radius r and height h is
Volume $ = \dfrac{1}{3}\pi {r^2}h$
Substituting r and h values in the above formula, we get
$ \Rightarrow Volume = \dfrac{1}{3}\pi {\left( {4.5} \right)^2}9 = 190.85c{m^3}$
$\therefore $ The volume of the largest right circular cone formed from the given cube is $190.85c{m^3}$
Note:
Here the base of the cone will be the circle inscribed in the face of the cube and its height will be equal to the edge length of the cube. We need to visualize the given problem in geometrical structures to solve the problem easily. When we represent the given problem in graphical form it looks similar to the below figure.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE