Question

The total area of sheet required to make an open cone of height 24 cm and radius 7 cm is
a.470 $c{m^2}$
b.450$c{m^2}$
c.425$c{m^2}$
d.550$c{m^2}$

Answer 1

Hint: We are asked to find the area of the open cone so it is enough to find the curved surface of the cone , whose formula is $\pi rl{\text{ }}sq.units$. We are only given the height and radius of the cone but we need to find the slant height using the formula $l = \sqrt {{h^2} + {r^2}} $

Complete step-by-step answer:
We are asked to find the area of sheet to make a cone
And we are mentioned it is a open cone so it is enough to find the curved surface area
And we are given that the height of the cone is 24 cm and radius is 7 cm

Now let's find the curved surface area of the cone
The curved surface area of the cone is given by the formula $\pi rl{\text{ }}sq.units$
But here we do not have the slant height l
The slant height is given by the formula
$ \Rightarrow l = \sqrt {{h^2} + {r^2}} $
Here we know that h = 24 cm and r = 7 cm
$
   \Rightarrow l = \sqrt {{{24}^2} + {7^2}} \\
   \Rightarrow l = \sqrt {576 + 49} \\
   \Rightarrow l = \sqrt {625} = 25cm \\
$
Using this lets find the curved surface area
$
   \Rightarrow CSA = \pi rl \\
   \Rightarrow CSA = \dfrac{{22}}{7}*7*25 \\
   \Rightarrow CSA = 22*25 \\
   \Rightarrow CSA = 550c{m^2} \\
$
Therefore the area of sheet required is 550$c{m^2}$
The correct option is d.
Note: Many students tend to use the height in the place of slant height , but it gives you the wrong solution. If we are asked for a closed cone then we need to find the total surface area of the cone.