Answer
Verified
417k+ 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
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
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
When people say No pun intended what does that mea class 8 english CBSE