Chapter 12.5, Problem 9CYU

To determine

To find the volume of air accommodated by heating and cooling systems in the conical sky dome of National Corvette Museum in Bowling, Kentucky.

Answer to Problem 9CYU

  $V\approx 513,330$ cubic feet (approximately)

Explanation of Solution

Given:

  

Height $(h)$ of the sky dome $=100$ feet Area $(B)$ of the base of the sky dome $=15,400$ square feet

Formula used:

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

where $B=\pi r^2$ is the area of the base and $h$ is the height of the cone.

Calculation: For the volume ( $V$ ) of the conical sky dome,

  $V=\frac{1}{3}Bh$

Put the values of $B=15400$ and $h=100$ ,

  $\Rightarrow \frac{1}{3}\times 15400\times 100$

  $\left[\pi =3.14\right]$

  $\Rightarrow \frac{1540000}{3}$

  $\Rightarrow V\approx 513,330$ cubic feet

Conclusion:

Therefore, the volume of the given cone is $513,330$ cubic feet (approximately).