Question

Peter has a cylindrical block of wood od diameter 6 cm and height 18 cm. He glues the base to a board, but wants to paint the rest of the block. He wants to paint the bottom half of the wood black and the top half white.
a) Calculate the surface area of the block that Peter will paint black.
b) Calculate the surface area of the block that Peter will paint white.

The black paint will cost Peter $0.03 for every 12 cm^2 painted and the white paint will cost Peter $0.04 for every 15 cm^2 painted.

c) If b represents the area of the black surface and w represents the white surface, write an expression for the cost C of painting the block in terms of b and w.

d) Calculate the value of C for Peter's block.

e) Determine whether or not Peter could paint his entire block white for less than or equal to $1.00.

Please could you help me check my answer please, please??

a) black:
area of circle C= 18.849 cm
area of rectange 9x18.849 = 170 cm^2

b) white:
169.641 + 28.274 = 198 cm^2

c) C= b(0.03/12) + w(0.04/15)

d)value of block is:
169,641 x0.03 $ / 12 = 0.42 $
197.901 X 0.04 $/ 15 = 0.527736 $

0.42 + 0.527736 = 0.947736 $
Peter could paint his entire block less than to $1.oo.

Thak you so much for checking and helping:)))

Answer 1

area of top circle T: pi*3^2 = 9pi = 28.27
area of sides S: pi*6*18 = 108pi = 339.29

(a) black = S/2 = 169.645
(b) white: T + S/2 = 197.915
(c) C = (.03/12)b + (.04/15)w
(d) C = .424 + .526 = 0.95
(e) yes

Aside from your typo on C, I pretty much agree with your figures.

Answer 2

Hi Steve, thank you so much for everything:)))
Have a very nice day