Amy needs to rust-proof a wrought-iron fence made of a rail that is a 1 cm thick by 4 cm wide by 102 cm long rectangular prism supported by posts that are 2 cm by 2 cm by 1 m high rectangular prisms. The posts are spaced 8 cm apart, attach to the bottom of the rail, and are embedded in cement. How much exposed surface area needs to be rust-proofed?
+128475
If I didn't make an error...
Lateral surface area to be covered of upright 11 posts =
Note that 1 m = 100 cm
11 * [ 4* 100 cm * 2 cm] =
11 [800 cm^2 ] = =
8800 cm^2
Suface area of top rail to be coated =
( Lateral surface area of rail ) - area where the upright post meets the top rail
(Area at two ends of the top rail + lateral surface area of rail ) - 11 (2cm *2cm) =
2 ( 1cm* 4cm) + 2*102 cm ( 1cm + 4 cm ) - 11 ( 4 cm^2) =
2 (4cm^2) + 204cm (5cm) - 44 cm^2 =
8cm^2 + 1020cm^2 - 44cm^2 = 984 cm^2
Total suface area to be covered = [ 8800+ 984] cm^2 = 9784 cm^2
