Answer to Question #147886 in Trigonometry for yui

Question

(NOS. 6-8) PROBLEM 2. Twelve concrete cylindrical columns of a building are to be covered by aluminium cladding. Each pillar has a diameter of 70 cm and height of 7m.

_______________________ 6) How much concrete is needed to construct the concrete 12 columns in m3?


______________________ 7) What is the total lateral surface area of the 12 columns in m2?



______________________ 8) If one sheet of aluminum cladding is 1.2m by 2.4m, how many
sheets of aluminum is needed to cover the 12 columns?

Answer 1

Solution.

$d=70 cm=0.7 m; \newline h=7m; \newline n=12 (columns).$

6) The volume of concrete for one column is:

$V_c=\pi*r^2*h,$ where $r=d/2=0.7/2=0.35 (m);$

$V_c=3.14*0.1225*7=2.69 (m^3).$

The volume of concrete for 12 columns is:

$V=n*V_c; \newline V= 12*2.69=32.28 (m^3).$

Answer: $V=32.28 m^3.$

7) Lateral surface area of one column is:

$S_c(lateral)=2\pi*r*h; \newline S_c(lateral)=2*3.14*0.35*7=15.386 (m^2).$

Lateral surface area of 12 columns is:

$S(lateral)=n*S_c(lateral); \newline S(lateral)=12*15.386=184.632 (m^2).$

Answer: $S(lateral)=184.632 m^2.$

8) Let the width w of aluminum cladding is 1.2 m and the length l is 2.4 m.

Area of one cladding is:

$S_{cl}=w*l; \newline S_{cl}=1.2*2.4=2.88 (m^2).$

Total surface area of one column is:

$S_c(total)=S_c(lateral)+2\pi*r^2.$

Total surface area of 12 columns is:

$S(total)=S(lateral)+12*2\pi*r^2; \newline S(total)=184.632+12*2*3.14*0.1225=\newline=184.632+9.2316=193.86(m^2).$

Number of sheets of aluminum to cover 12 columns is:

$Num=S(total)/S_{cl}; \newline Num=193.86/2.88=67.31(sheets).$

Answer: $67.31(sheets).$