# What is the Volume of Cone for radius is 15 & height is 20

The volume is 4712.389 and surface area is 1884.9556 of a cone having base radius of 15 and height of 20, refer the calculation summary and work with steps for detailed explanation.

Calculation Summary | |
---|---|

Radius | 15 in |

Height | 20 in |

Volume V | 4712.389 in³ |

Slant Height | 25 in |

Surface Area | 1884.9556 in² |

Lateral Surface Area | 1178.0972 in² |

## Work with Steps to Find Volume & Surface Area of Cone for r = 15 & h = 20

__Question:__

The radius & height of a cone measured as 15 inches and 20 inches respectively, find what is the volume, slanting height, lateral surface and the surface area of that cone?

__workout :__

step 1 Address the formula, input parmaeters & values

Radius = 15 in

Height = 20 in

step 2 Apply radius and height values in below volume formula

Volume V = πr²h/3

= π x (15)² x 20/3in³

= 3.1416 x (225) x 20/3in³

= 14137.167/3in³

Volume V = 4712.389 in³

step 3 Apply radius and height in slant height formula

Slant height L = √(r² + h²) in²

= √(15² + 20²) in²

= √(225 + 400) in²

= √625 in

Slant height h = 25 in

step 4 Find surface area using radius, height and slant height

Surface Area = πr(r + √r² + h²)

= πr(r + slant height)

= 3.1416 x 15 (15 + 25) in²

= 3.1416 x 15 x 40 in²

Surface Area = 1884.9556 in²

step 5 Find lateral surface area using radius, height, ad slant height

Lateral Surafce Area = π r√r² + h²

= π x r x slant height

= 3.1416 x 15 x 25 in²

Lateral Surafce Area = 1178.0972 in²