Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.
Last updated date: 27th Mar 2023
•
Total views: 308.1k
•
Views today: 2.85k
Answer
308.1k+ 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
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
