Cylinder has a radius of 4 in. and height of 13. Cardboard container cost 10 cents per sq. ft. and the plastic cost 50 cents per sq. ft. what is the cost of container? Container is made out of...

Cylinder has a radius of 4 in. and height of 13.

Cardboard container cost 10 cents per sq. ft. and the plastic cost 50 cents per sq. ft. what is the cost of container? Container is made out of cardboard except for top which is plastic.

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oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on

cost_palstic = Bottom_surface X cost

Bottom_surface = `pi r^2=50,24 In ^2` `=0,348 ft^2`

Thus  cost  palstic is  `50 (cent) /ft^2`

`C_p=17.40_C`

`S_c= pi r (2h +r)=376,8 In^2=2,62 ft^2`

`C_c=26.20_C`

`C_T=C_p+C_c=43.60_C`

``

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

Curved surface area of cylinder= `2pirh`  sq inch.    (i)

Area of the bottom of the cylinder=`pi r^2`  sq.inch     (ii)

Area of the top of cylinder = Area of the bottom of the cylinder

Area of the top of cylinder= (22/7)(4^2) sq inch

                                    =(352/7) sq. inch             (iii)

Total are of required card board= (i)+(ii)

=`2pirh+pir^2`

`=pir(2h+r)` sq. in

= (88/7)(2x13+4) sq inch

=2640/7 sq.inch                                               (iv)

1 foot =12 inch

1 sq feet =12 x 12 sq inch

             =144 sq inch

144 sq inch card board cost = 10 cent

1 sq inch     card board cost = 10/144 cent

2640/7 sq. inch card board cost= (2640/7)(10/144)=26.19 cent     (v)

 

144 sq inch plastic cost= 50 cent

1 sq. inch plastic cost= 50/144 cent

(352/7) sq. inch cost= (352/7)(50/144)=17.46 cent              (vi)

cost of container= (v)+(vi)=26.19+17.46

=43.65 cent

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