Question

The base radius of an ice cream cone is 3.5 cm and the slant height is 6.5 cm. What is the capacity of the ice cream cone and its surface area (to the nearest hundredth)?

Lateral Area = _____ cm2

A) 70.26
B) 71.44
C) 109.9

Volume = _____ cm3

A) 70.26
B) 71.44
C) 109.9

Answer 1

Lateral area of cone =
`\pi rs+\pi r^(2)`

volume of cone is
`70.26cm^(3)`

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 =
`\pi rs+\pi r^(2)`

where r = radius of cone

s= slant height

`\pi =3.14`

now putting values in formula we get :

`3.14*3.5*6.5 + 3.14*3.5^(2))`

`109.9`

Thus the surface area of cone is
`109.9cm^(2)`

Hence lateral are =
`109.9cm^(2)`

Now formula of volume of cone =
`(1)/(3) \pi r^(2) h` ---(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 :

`P^(2) +B^(2) =H^(2)`

`P^(2) +3.5^(2) =6.5^(2)`

`P^(2) +12.25 =42.25`

`P^(2)  =42.25 - 12.25`

`P^(2)  =30`

`P=√(30)`

Thus height of cone is
`P=√(30) cm`

putting values in (a)

⇒
`(1)/(3)*3.14* 3.5^(2)*√(30)`

⇒
`(1)/(3)*3.14* 12.25*√(30)`

⇒
`70.26`

Thus the volume of cone is
`70.26cm^(3)`

Hence ,the capacity of the ice cream cone is
`70.26cm^(3)`