Chapter SH, Problem 11.7MPS

i.

To determine

Calculate the circumference of the space covered by fountain.

  

Answer to Problem 11.7MPS

Circumference of the space covered by fountain is $125.663ft$

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate circumference of the given figure.

We have given inside diameter of 16 ft and thickness of 4 ft. From this, outside diameter of, 16+4+4=24 ft.

Therefore, Inside radius = 8ft

Outside radius = 12ft

Area of circular ring is calculated as, $$

  $\begin{array}{l}Circumferenceofcircularring=2\pi (R+r)\\ =2\pi (12+8)\\ Circumferenceofcircularring=125.663ft\end{array}$

Conclusion:

Therefore, we are able to find circumference of circular ring.

ii.

To determine

Calculate the area of space covered by fountain.

  

Answer to Problem 11.7MPS

Area of space covered by fountain is $251.327f{t}^2$

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate circumference of the given figure.

We have given inside diameter of 16 ft and thickness of 4 ft. From this, outside diameter of, 16+4+4=24 ft.

Therefore, Inside radius = 8ft

Outside radius = 12ft

Area of circular ring is calculated as, $$

  $\begin{array}{l}Areaofcircularring=\pi (R+r)(R-r)\\ =\pi (12+8)(12-8)\\ Areaofcircularring=251.327f{t}^2\end{array}$

Conclusion:

Therefore, we are able to find area of space covered by fountain.

iii.

To determine

Calculate the cost of stone path for walkway.

  

Answer to Problem 11.7MPS

Total cost of stone path for walkway is $439.822\$$

Explanation of Solution

Given:

  

Cost of stone per square foot = 1.75$

Calculations:

Here, we have to calculate cost of the stone path for walkway.

Here we have area of circular path is 251.327 sq. ft

Total cost of stone path can be calculated as,

  $\begin{array}{l}Total\cos tofstonepathway=Area\times \cos tpersquarefeet\\ =251.327\times 1.75\\ =439.822\$\end{array}$

Conclusion:

Therefore, we are able to find total cost of stone path for walkway.