Find the volume of a right circular cone with height h and radius of base r.

Introduce a coordinate system to measure the height of the cone.

Using similar triangles, it can be shown that the radius of the cross-section is r(h-x)/h.

Hence, the area of the circle A(x) = π*(radius)

The volume of the cone is

You may also remember that the formula for the volume of a cone is 1/3*(area of base)*height = 1/3*πr

Using the TI-83/84

Measure the height h and the radius r of a cone. Store these values in H and R.

An example.

Suppose my cone has a radius of 3 cm and a height of 5 cm.

3→R_{ }^{ } |

5→H_{ }^{ } |

\Y1=π(R(H-X)/H)^{2}_{ }^{ } |

\Y2=1/3*πR^{2}H_{ }^{ } |

You find fnInt under MATH. From the home screen, enter

fnInt(Y1,X,0,H)_{ }^{ }_{ }^{ } |
ENTER_{ }^{ } |
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47.1238898_{ }^{ } |
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Y2_{ }^{ } |
ENTER_{ }^{ } |
|||||||

47.1238898_{ }^{ } |

Task.

You have a Dixie cup. Find its volume using rice, using the regular formula, and using calculus!

Calculus Index