area of right circular cylinder

Question

The radius and the height of a right circular cone are respectively 21 cm and 28 cm .From its base to a height of 14 cm., the portion of the curved surface was painted golden and the upper portion was painted silver. Find the total cost of painting the whole curved surface at the rate of $2 per cm^{2 for} the golden color and at the rate of $1 per cm² for the silver color.

Answer 1

Dear Sanjay,

 

   The title of this problem says, "Circular Cylinder," but the story problem says, "right circular cone."  These are two different objects.  The right cylinder is like a soda can, but the right circular cone is like the snow cone that holds the ice.  I am going to assume that you mean the snow cone shape with a perpendicular height from the peak or vertex to the circular base.  The circular base is one piece, which is silver.  The curved piece that makes the cone part is the second part.

 

 Given:  r=21      h=28

Area of circular base, A=πr² =π(21)² = 138.23 sq. cm.      138.23 * $1.00= $138.23 to paint the circular base

$1= 1sq. cm for the silver base

 

Area of curved surface all the way up the height=lateral area= π*r*s, where s =slant height, which is the length

 

of a side.  Since that side could be the hypotenuse of a right triangle, we have s=√(r²+h²).

 

 

 Substitute values into the equation:   s=^√(21²⁺(28)²⁾ =35 cm     lateral length

 

 

lateral area= π*r*s       π (21)(35)= 735(π)=2,309.07 Sq. cm        2309.07*$2=__________

 

$2= 1 sq. cm for the golden part

 

 

cost of circular base + cost of curved area all the way up to 14 cm= ______________Total cost

 

 

I will let you complete the problem.  If I helped you, please give me a thumbs up.

 

                                                                            Susan C.

Answer 2

SA = πr²h

 

SA = π(21)²(28)

SA = π(441)(28)

SA = π(12348)

SA ≈ 38792.3861

 

The two equal sections are each approximately 19,396.19 cm²

 

The silver portion costs $19,396.19 and the gold portion costs $38,792.39.