Question #147886
(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?
1
Expert's answer
2020-12-01T20:44:43-0500

Solution.

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


6) The volume of concrete for one column is:

Vc=πr2h,V_c=\pi*r^2*h, where r=d/2=0.7/2=0.35(m);r=d/2=0.7/2=0.35 (m);

Vc=3.140.12257=2.69(m3).V_c=3.14*0.1225*7=2.69 (m^3).

The volume of concrete for 12 columns is:

V=nVc;V=122.69=32.28(m3).V=n*V_c; \newline V= 12*2.69=32.28 (m^3).

Answer: V=32.28m3.V=32.28 m^3.


7) Lateral surface area of one column is:

Sc(lateral)=2πrh;Sc(lateral)=23.140.357=15.386(m2).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)=nSc(lateral);S(lateral)=1215.386=184.632(m2).S(lateral)=n*S_c(lateral); \newline S(lateral)=12*15.386=184.632 (m^2).

Answer: S(lateral)=184.632m2.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:

Scl=wl;Scl=1.22.4=2.88(m2).S_{cl}=w*l; \newline S_{cl}=1.2*2.4=2.88 (m^2).

Total surface area of one column is:

Sc(total)=Sc(lateral)+2πr2.S_c(total)=S_c(lateral)+2\pi*r^2.

Total surface area of 12 columns is:

S(total)=S(lateral)+122πr2;S(total)=184.632+1223.140.1225==184.632+9.2316=193.86(m2).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)/Scl;Num=193.86/2.88=67.31(sheets).Num=S(total)/S_{cl}; \newline Num=193.86/2.88=67.31(sheets).

Answer: 67.31(sheets).67.31(sheets).


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