Find the volume, curved surface area and the total surface area of a cone having base radius $$35\ cm$$ and height $$12\ cm$$.
It is given that
Radius of the cone $$=35\ cm$$
Height of the cone $$=12\ cm$$
We know that
Volume of the cone $$=\dfrac{1}{3}\pi r^{2}h$$
By substituting the values
Volume of the cone $$=\dfrac{1}{3}\times \dfrac{22}{7}\times 35^{2}\times 12$$
On further calculation
Volume of the cone $$=15400\ cm^{2}$$
We know that
Slant height $$l=\sqrt {(r^{2}+h^{2})}$$
By substituting the values
$$l=\sqrt{ (35^{2}+12^{2})}$$
On further calculation
$$l=\sqrt{ 1369}$$
So we get
$$l=37\ cm$$
We know that
Curved surface area of a cone $$=\pi rl$$
By substituting the values
Total surface area of cone $$=\dfrac{22}{7}\times 35\times (37+35)$$
On further calculation
Total surface area of cone $$=22\times 5\times 72$$
So we get
Total surface area of cone $$=7920\ cm^{2}$$