Question

A right circular cone is 5.8 cm high and the radius of its base is 3.4 cm. It is melted and recast into a right circular cone with radius of its base 1.7 cm. Find its height.
A. 20.2 cm
B. 21.2 cm
C. 23.2 cm
D. 22.2 cm

Answer 1

Hint: In this question read the given information carefully and identify the dimensions of the right circular cone and also remember that the volume of the circular cone will be the same after changing its dimensions. Using these extra information will help you to approach the solution of the question.

Complete step-by-step answer:

According to the given information we know that a right cone with dimensions height (h₁) 5.8 cm and radius (r₁) as the base of right circular cone is 3.4 cm is melted into a right circular cone changing its dimension and the radius (r₂) is 1.7 cm as the base
Since we know that the volume of right circular will remain same after melting and recasting it to right circular cone i.e. Volume of circular cone of radius 3.4cm = volume of right circular cone of radius 1.7 cm
Since we know that the volume of right circular cone is given by \[\dfrac{1}{3}\pi {r^2}h\] here r is the radius of the right circular cone and h is the height of the right circular cone
Therefore \[\dfrac{1}{3}\pi {r_1}^2{h_1} = \dfrac{1}{3}\pi {r_2}^2{h_2}\]
Substituting the given values in the above equation we get
\[\dfrac{1}{3}\pi {\left( {3.4} \right)^2}\left( {5.8} \right) = \dfrac{1}{3}\pi {\left( {1.7} \right)^2}{h_2}\]
$ \Rightarrow $\[\left( {11.56} \right)\left( {5.8} \right) = \left( {2.89} \right){h_2}\]
$ \Rightarrow $\[{h_2} = \dfrac{{67.048}}{{2.89}}\]
$ \Rightarrow $\[{h_2}\] = 23.2 cm
Therefore the height of a re-casted right circular cone will be 23.2 cm
Hence option C is the correct option.

Note: The above question was totally based on the right circular cone which have some properties which makes it different from a general cone which can be defined as the cone shape body in which the axis of cone is perpendicular to the base but other properties of right circular cone is same as the common cone such as it has a base which is in circular shape, it has only one face which is the base of circular shape and it has a single vertex point.