How many metres of cloth, $$2.5\ m$$, wide will be required to make a conical tent whose base radius is $$7\ m$$ and height $$24\ m$$?
It is given that
Radius of the conical tent $$=7m$$
Height of the conical tent $$=24\ m$$
We know that
Slant height $$l=\sqrt{ (r^{2}+h^{2})}$$
By substituting the values
$$l=\sqrt {(7^{2}+24^{2})}$$
On further calculation
$$l=\sqrt {(49+576)}=\sqrt {625}$$
So we get
$$l=25\ m$$
We know that
Area of the cloth $$=\pi rl$$
By substituting the values
Area of the cloth $$=\dfrac{22}{7}\times 7\times 25$$
On further calculation
Area of the cloth $$=550\ m^{2}$$
We know that
length of the cloth = area/width
By substituting the values
Length of the cloth $$=\dfrac{550}{2.5}=220\ m$$
Therefore, $$220\ m$$ of cloth is required to make the conical tent.