Answer:
The side of the cube is 4.04 cm.
Step-by-step explanation:
Given:
A cone of diameter 6cm and height 7 cm is melted and recast into cube.
Now, to find the side of the cube.
So, to get the volume of cone we put formula:
Radius = [tex]\frac{Diameter}{2}=\frac{6}{2}=3\ cm.[/tex]
Height = 7 cm.
[tex]Volume =\pi r^{2} \frac{h}{3}[/tex]
Taking the value of π =3.14.
[tex]Volume =3.14\times 3^{2}\times \frac{7}{3}[/tex]
[tex]Volume =3.14\times 9\times \frac{7}{3}[/tex]
[tex]Volume =28.26\times \frac{7}{3}[/tex]
[tex]Volume=\frac{197.82}{3}[/tex]
[tex]Volume=65.94\ cm^3.[/tex]
As we know that after recast of any shape of a figure to another the volume remains the same.
Thus, the volume of melted and recast cube = 65.94 cm³.
Now, to get the side of the cube we put formula:
[tex]Volume = (side)^3.[/tex]
⇒ [tex]65.94=side^3.[/tex]
Using cube root on both sides we get:
⇒ [tex]4.04=side.[/tex]
Side = 4.04 cm.
Therefore, the side of the cube is 4.04 cm.
