How do you find surface area of a rectangular prism with length 8cm, width 5cm, and height 4cm with a hold diameter 2cm drilled through it?

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Answer 1 · 2018-08-04T05:44:03

#color(magenta)(T S A = 222 + 4 pi ~~ 234.5664 cm^2#

#"Lateral Surface area of a solid rectangular prism "A_l = 2 * (bh + hl)#

#"Base area of prism (Top + Bottom )" =A_(bp) = 2 l b#

#"Lateral Surface area of cylinder " A_c = 2 pi r h#

#"Base area of cylinder(Top + Bottom) " A_(bc) = 2pi r^2#

#"Given : " l = 8cm, b = 5cm, h = 4cm, r = 2cm#

#"L S A of rect. prism " A_l = 2 ( 8*5 + 4 * 8) = 144 cm^2#

#"L S A of cylinder " A_c = 2 pi (2/2) * 4 = 8 pi cm^2#

#"Base areas of rect. prism " = A_(bp) = 2 * 8 * 5 = 80 cm^2#

#"Base areas of cylinder " = A_(bc) = pi 2^2# = 4 pi cm^2#

#"Total Surface Area of the solid " T S A = A_l + A_c + A_(bp) - A_(bc)#

#color(magenta)(T S A = 144 + 8pi + 80 - 4 pi = 222 + 4 pi ~~ 234.5664 cm^2#