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:)))
To calculate the surface area of the block that Peter will paint black, we need to find the area of the circular base and the lateral surface area of the cylinder.
a) The area of the circular base can be calculated using the formula A = πr^2, where r is the radius of the base (half the diameter). In this case, the diameter is 6 cm, so the radius is 3 cm. Thus, the area of the circular base is A = π(3 cm)^2 = 9π cm^2 ≈ 28.274 cm^2.
The lateral surface area of the cylinder can be calculated using the formula A = 2πrh, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is 3 cm and the height is 18 cm. Thus, the lateral surface area is A = 2π(3 cm)(18 cm) = 36π cm^2 ≈ 113.097 cm^2.
To calculate the surface area of the block that Peter will paint black, we add the area of the circular base and the lateral surface area: black area = 28.274 cm^2 + 113.097 cm^2 = 141.371 cm^2.
b) The surface area of the block that Peter will paint white is equal to the total surface area of the block minus the surface area that Peter will paint black.
To calculate the total surface area of the block, we add the area of the circular base, the lateral surface area, and the top circular face. Notice that the top face is the same as the circular base, so its area is also 28.274 cm^2.
Total surface area = 28.274 cm^2 + 113.097 cm^2 + 28.274 cm^2 = 169.641 cm^2.
Therefore, the surface area of the block that Peter will paint white is equal to the total surface area minus the black area: white area = 169.641 cm^2 - 141.371 cm^2 = 28.27 cm^2.
c) The cost of painting the block can be expressed as follows:
C = (black area) * (cost per cm^2 for black paint) + (white area) * (cost per cm^2 for white paint).
Substituting the values, C = b(0.03/12) + w(0.04/15), where b represents the black area and w represents the white area.
d) To calculate the value of C, we substitute the values we found in parts a) and b) into the expression for C:
C = (141.371 cm^2) * (0.03/12) + (28.27 cm^2) * (0.04/15)
C ≈ 0.3528571 $ + 0.037893333 $
C ≈ 0.3907504 $
e) To determine whether Peter could paint his entire block white for less than or equal to $1.00, we check if the value of C is less than or equal to $1.00. In this case, C ≈ $0.3907504, which is less than $1.00, so Peter could paint his entire block white for less than or equal to $1.00.
Your answers seem to be correct. Well done!