# Conical Frustum

## 038 Review Problem - Circular log with non-uniform cross-section

**Problem 38**

A log 18 ft. long is 2 ft. in diameter at the top end and 3 ft. in diameter at the butt end.

- How many cubic feet of wood does the log contain?
- How many cubic feet are there in the largest piece of timber of square cross section that can be cut from the log?
- How many cubic feet are in the largest piece of square timber of the same size throughout its whole length?
- How many board feet does the piece of timber in (c), a board foot being equivalent to a board 1 ft. square and 1 in. thick?

Hint: In (b) the larger end is the square ABCD. What is the smaller end? In (c) one end is the square EFGH. What is the other end?

## 032 Review Problem - How many cups of coffee a coffee pot can hold?

**Problem 32**

A coffee pot is 5 in. deep, 4-1/2 in. in diameter at the top, and 5-3/4 in. in diameter at the bottom. How many cups of coffee will it hold if 6 cups equal 1 quart? Answer to the nearest whole number.

## 022 Review Problem - Tin required to create a funnel

**Problem 22**

How many square feet of tin are required to make a funnel, if the diameters of the top and bottom are 28 in. and 14 in., respectively, and the height is 24 in.?

## 013 Review Problem - Volume of water inside the Venturi meter

**Problem 13**

The accompanying figure represents the longitudinal view of a Venturi meter, a device designed to measure the flow of water in pipes. If the throat of the of the meter is 6 in. long and has an inside diameter of 4 in., find the volume of water in the meter which is used in 12-in. pipe line if the altitudes of the tapering parts are in the ratio 1:3 and the smaller altitude measures 12 in.

## Derivation of formula for volume of a frustum of pyramid/cone

**Frustum of a pyramid and frustum of a cone**

The formula for frustum of a pyramid or frustum of a cone is given by

Where:

h = perpendicular distance between A_{1} and A_{2} (h is called the altitude of the frustum)

A_{1} = area of the lower base

A_{2} = area of the upper base

Note that A_{1} and A_{2} are parallel to each other.