Question

a right circular cylinder of maximum volume is cut from a solid cube of edge 14 cm. the total surface of the cylinder is?

Answer 1

Solution :-

A right circular cylinder of maximum volume is cut from a solid cube of edge 14 cm. 

So,

Length of the Edge of the given cube = Diameter of the cylinder

Also, Edge (Height) of the given cube = Height of the cylinder 

Diameter = 14 cm

Then, radius = 14/2 = 7 cm

Total surface area of the cylinder = 2πrh + 2πr²

⇒ 2*22/7*7*14 + 2*22/7*7*7

⇒ (44*14) + (44*7) 

⇒ 616 cm² + 308 cm²

Total surface area of the cylinder = 924 cm²

Answer.

Answer 2

As the maximum volume of the cylinder in cut from the solid cube ,the edge of which is equal to the 14 cm so here we can assume the two things easily,

The  length of edge of cube will be equal to diameter of the cylinder
And
Height (edge ) of the cube will be equal to the height of the cylinder.
 
So we can say that diameter is equal to 14 cm 

As we know that radius= Diameter/2 = 14//2 = 7cm will be the radius.

We know that there are two ends in the cylinder so their total surface area will be the the surface of both
 .
So, Total surface area of the cylinder = 2*π*r*h +2πr²
So by putting values                  =2*22/7*7*14 + 2*22/7*49
 
Total surface area of cylinder    =616+308 = 924cm2 will be our answer.