Chapter 12.5, Problem 31PPS

a.

To determine

To determine the change affecting the volume of the cone

Answer to Problem 31PPS

  $V=301.592{\text{ centimeter}}^3$

Explanation of Solution

Given:

Radius of cone $=4$ centimeter

Height of cone $=9$ centimeter

The height is doubled.

Formula used:

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

  $\left[r=\text{radius, }h\text{=}\text{height}\right]$

Calculation:

Given, radius of cone $=4$ centimeter

Height of cone $=9$ centimeter

When height is doubled,

  $h=2H=18[h=\text{height of the cone}]$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(4)}^2\times 18$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 904.778$

  $\Rightarrow$ Volume of the cone $V=301.592{\text{ centimeter}}^3$

Conclusion:

Therefore, the change affecting the volume of the cone when height is doubled $V=301.592{\text{ centimeter}}^3$ .

b.

To determine

To determine the change affecting the volume of the cone

Answer to Problem 31PPS

  $V=603.185{\text{ centimeter}}^3$

Explanation of Solution

Given:

Radius of cone $=4$ centimeter

Height of cone $=9$ centimeter

The radius is doubled.

Formula used:

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

  $\left[r=\text{radius, }h\text{=}\text{height}\right]$

Calculation:

Given, radius of cone $=4$ centimeter

Height of cone $=9$ centimeter

When radius is doubled,

  $r=2R=2\times 4[R=\text{radius of the cone}]$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(8)}^2\times 9$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 1809.557$

  $\Rightarrow$ Volume of the cone $V=603.185{\text{ centimeter}}^3$

Conclusion:

Therefore, the change affecting the volume of the cone when radius is doubled

  $V=603.185{\text{ centimeter}}^3$ .

c.

To determine

To determine the change affecting the volume of the cone

Answer to Problem 31PPS

  $V=1206.371{\text{ centimeter}}^3$

Explanation of Solution

Given:

Radius of cone $=4$ centimeter

Height of cone $=9$ centimeter

The height and the radius are doubled.

Formula used:

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

  $\left[r=\text{radius, }h\text{=}\text{height}\right]$

Calculation:

Radius of cone $=4$ centimeter

Height of cone $=9$ centimeter

When height and the radius are doubled

  $r=2R=2\times 4[R=\text{radius of the cone}]$ and $h=2H=18[h=\text{height of the cone}].$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(8)}^2\times 18$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 3619.114$

  $\Rightarrow$ Volume of the cone $V=1206.371{\text{ centimeter}}^3$

Conclusion:

Therefore, the change affecting the volume of the cone when the height and the radius are doubled is $V=1206.371{\text{ centimeter}}^3$ .