Question

How to fine the volume and surface are in a cone

Answer 1

PROJECT WORK:

Assumption:

For the given cone, assuming

`\begin{gathered} r\text{ = 10 m} \\ h\text{ = 12 m} \end{gathered}`

Slant height of cone is calculated as,

`\begin{gathered} l^2\text{ = r}^2\text{ + h}^2 \\ l^2\text{ = 10}^2\text{ + 12}^2 \\ l^2\text{ = 100 + 144} \\ l^2\text{ = 244} \\ l\text{ = 15.62 m} \end{gathered}`

Required:

Surface area and volume of cone.

Step-by-step explanation:

The surface area of cone is given as,

`\begin{gathered} Surface\text{ area = }\pi r(l+r) \\ Surface\text{ area = 3.14}*\text{ 10\lparen15.62 + 10\rparen} \\ Surface\text{ area =3.14}*\text{ 10\lparen25.62\rparen} \\ Surface\text{ area = 3.14}*\text{ 256.2} \\ Surface\text{ area = 804.468 m}^2 \end{gathered}`

Volume of cone is calculated as,

`\begin{gathered} Volume\text{ = }(1)/(3)\pi r^2h \\ Volume\text{ = }(1)/(3)*3.14*10*10*12 \\ Volume\text{ = }(3768)/(3) \\ Volume\text{ = 1256 m}^3 \end{gathered}`

Answer:

Thus the volume of the cone is 1256 cu.m.

The surface area of the cone is 804.468 sq.m.