Chapter 1.7, Problem 36PPS

a.

To determine

To create a table showing volume of cone

Answer to Problem 36PPS

The table is as follows

Explanation of Solution

Given information:

Radius of cone, r = (1, 8)

Height of cone= 3

Formula used:

Volume of cone = $\frac{1}{3}\pi r^{2}h$

Calculation:

Substituting values in equation,

Table is

Radius	Formula=$\frac{1}{3}\pi r^{2}h$	values
1	$\frac{1}{3}\pi {(1)}^{2}3$	3.14
2	$\frac{1}{3}\pi {(2)}^{2}3$	12.57
3	$\frac{1}{3}\pi {(3)}^{2}3$	28.27
4	$\frac{1}{3}\pi {(4)}^{2}3$	50.27
5	$\frac{1}{3}\pi {(5)}^{2}3$	78.54
6	$\frac{1}{3}\pi {(6)}^{2}3$	113.1
7	$\frac{1}{3}\pi {(7)}^{2}3$	153.94
8	$\frac{1}{3}\pi {(8)}^{2}3$	201.06

b.

To determine

To make a graph

Explanation of Solution

Given information:

Tabular data of volume

Graph:

  

c.

To determine

To make a conjecture

Answer to Problem 36PPS

Explanation of Solution

Given information:

A cone

Concluding by doubling the graph, a conjecture which can be made is:

The volume increases 4 times if the radius is doubled.

d.

To determine

To write an expression on doubling radius

Answer to Problem 36PPS

The expression is $\frac{4}{3}\pi {(r)}^{2}h$ .

Explanation of Solution

Given information:

Radius is doubled, i.e. 2r

Formula used:

Volume of cone = $\frac{1}{3}\pi r^{2}h$

Calculation:

Substituting value in formula,

Volume= $\frac{1}{3}\pi {(2r)}^{2}h$

Solving,

Volume= $\frac{4}{3}\pi {(r)}^{2}h$

Hence, the expression is $\frac{4}{3}\pi {(r)}^{2}h$ .