Question

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

Answer 1

The area of metal sheet required to make this hollow closed cone would be equal to the total surface area of the cone.

The formula of the total surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as 

Total Surface Area = ` pi r(l+r)`

It is given that the vertical height ‘h’ = 24 cm and base radius ‘r’ = 7 cm.

To find the slant height ‘l’ we use the following relation

Slant height, l = `sqrt(r^2 + h^2)`

= `sqrt(7^2 + 24^2)`

= `sqrt(49 + 576)`

= ` sqrt(625)`

l = 25

Hence the slant height of the given cone is 25 cm.

Now, substituting the values of r = 7 cm and slant height l = 25 cm and using  ` pi = 22/7` in the specified formula,

Total Surface Area = `((22)(7)(7+25))/7`

= (22) (32)

= 704

Therefore the total area of the metal sheet required to make the closed hollow cone is equal to  704 cm² .