Answer:
Lateral area of cone = [tex]\pi rs+\pi r^{2}[/tex]
volume of cone is [tex]70.26cm^{3}[/tex]
Step-by-step explanation:
Given : radius of cone(r) = 3.5 cm
Slant height (s) = 6.5 cm
To Find : The capacity of the ice cream cone(volume of cone ) and its surface area
Solution :
To find surface area and volume we will use the formulas of area and volume of cone i.e.
Surface area of cone = [tex]\pi rs+\pi r^{2}[/tex]
where r = radius of cone
s= slant height
[tex]\pi =3.14[/tex]
now putting values in formula we get :
[tex]3.14*3.5*6.5 + 3.14*3.5^{2})[/tex]
[tex]109.9[/tex]
Thus the surface area of cone is [tex]109.9cm^{2}[/tex]
Hence lateral are = [tex]109.9cm^{2}[/tex]
Now formula of volume of cone =[tex]\frac{1}{3} \pi r^{2} h[/tex] ---(a)
where r = radius of cone
h = height of cone
first we need to calculate the height of cone
refer to attached figure we can see that right angled triangle is formed with radius , height and slant height
So, To calculate height we will use Pythagoras theorem :
[tex]P^{2} +B^{2} =H^{2}[/tex]
[tex]P^{2} +3.5^{2} =6.5^{2}[/tex]
[tex]P^{2} +12.25 =42.25[/tex]
[tex]P^{2} =42.25 - 12.25[/tex]
[tex]P^{2} =30 [/tex]
[tex]P=\sqrt{30}[/tex]
Thus height of cone is [tex]P=\sqrt{30} cm[/tex]
putting values in (a)
⇒[tex]\frac{1}{3}*3.14* 3.5^{2}*\sqrt{30}[/tex]
⇒[tex]\frac{1}{3}*3.14* 12.25*\sqrt{30}[/tex]
⇒[tex]70.26[/tex]
Thus the volume of cone is [tex]70.26cm^{3}[/tex]
Hence ,the capacity of the ice cream cone is [tex]70.26cm^{3}[/tex]
