A **cylinder** is a circular prism. As with other prisms, the volume of a cylinder can be calculated using the cross-sectional area x length.

Th cross-section of a cylinder is a circle. As the area of a circle =`πr^2`, the volume of a cylinder is `πr^2l`, where `r` is the radius of the circular end, and `l` is the length of the cylinder.

What is the volume of a cylinder with a diameter of 4cm and a length of 42cm? Give your answer correct to 1 decimal place.

For a circle: | Area | `= pir^2` |

Substitute | `A` | `= pi xx 2^2` |

`= 4pi` |

The cross-sectional area is `4pi`

For a cylinder: | Volume | = area xx length |

Substitute | V | `= 4pi xx 42` |

`= 527.79` |

Answer: 527.8 cm^{3}

What is the diameter of a cylinder with a volume of 1000cm^{3} and a length of 100cm? Give the answer correct to 1 decimal place.

For a Cylinder | Volume | `= pir^2l` |

Substitute | `1000` | `= pir^2 xx 100` |

Divide both sides by 100 | 10 | `= pir^2` |

Divide both sides by `pi` | 3.183 | `= r^2` |

Square root | 1.784 | `= r` |

Answer: 1.8cm

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