Question

The base radius of an ice cream cone is 3.5 cm and the slant height is 6.5 cm. What is the capicity of the ice cream cone and it’s surface area?

Answer 1

The capacity of the cone is 70.26 cubic cm.

The surface area of cone is 109.96 square cm.

Explanation:

We have been given that the base radius of an ice-cream cone is 3.5 cm and the slant height is 6.5 cm.

The capacity of the ice cream cone will be equal to volume of cone.

First of all, we will find height of our given cone using Pythagoras theorem.

`h^2=l^2-r^2`, where,

h = Height of cone,

l = Slant height of cone,

r = Radius of cone.

`h^2=6.5^2-3.5^2`

`h^2=42.25-12.25`

`h^2=30`

`h=√(30)`

`\text{Volume of cone}=(\pi r^2 h)/(3)`

Upon substituting our given values in volume formula we will get,

`\text{Volume of cone}=(\pi*3.5^2*√(30))/(3)`

`\text{Volume of cone}=(210.788)/(3)`

`\text{Volume of cone}=70.262\approx 70.26`

Therefore, the capacity of the cone is 70.26 cubic cm.

`\text{Surface area of cone}=\pi rl+\pi r^2`

Upon substituting our given values in surface area formula we will get,

`\text{Surface area of cone}=\pi*3.5*6.5+\pi *3.5^2`

`\text{Surface area of cone}=\pi*3.5*6.5+\pi *12.25`

`\text{Surface area of cone}=71.471232+38.48451`

`\text{Surface area of cone}=109.955742\approx 109.96`

Therefore, the surface area of cone is 109.96 square cm.

Answer 2

Answer: Capacity = 70.227 Cube cm ( Approx )

Total Surface area = 109.9 square cm

Explanation:

Since the volume of a cone,

`V = (1)/(3) \pi r^2h`

Where r is the radius of the cone,

h is the height of the cone,

Here, radius, r = 3.5 cm

Height,
`h = √(6.5^2-3.5^2) =5.47722557505`

Thus, the volume of the cone,

`V = (1)/(3) \pi r^2h`

`=(1)/(3) * 3.14* (3.5)^2* 5.47722557505=70.2271605815\approx 70.227\text{ cube cm}`

And, Total surface area,

`A = \pi r l+\pi r^2`

Where l is the slant height of the cone,

Here, l = 6.5 cm

Thus, the curved surface area of the given cone,

`A = 3.14* 3.5* 6.5 + 3.14* (3.5)^2= 71.435+38.465=109.9\text{ square cm}`