# ACT Math 2.5 Plane Geometry

ACT Math Plane Geometry Drill 2, Problem 5. What is the surface area of a rigid circular cone with diameter = 10 and height = 12?

ACT Math | Plane Geometry |

ACT Mathematics | Plane Geometry |

Area and Volume | Area |

Coordinate Geometry | Conics |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Language | English Language |

Plane Geometry | Surface area |

Product Type | ACT Math |

### Transcript

surface area equals pi times r times the square root of the quantity radius squared plus height squared.

Well, they give us the height. Now we need the diameter to tell us what the radius is;

...and in a circle, here is the diameter -- the radius is just half of it. So if diameter is 10

half is 5.

Now just plug in the numbers.

It's pi times 5 times the square root quantity of 5 squared plus 12 squared which simplifies to

5 pi times the square root quantity 25 plus 144 or 169 -- and ooh magic number --

169 should trigger a bell in your head.

It is 13 squared.

So we have 5 times pi times 13 -- 5 times 13 is 65 so the answer is 65 pi.

Answer D.