# 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?

Aug 4, 2018

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

#### Explanation:

$\text{Lateral Surface area of a solid rectangular prism } {A}_{l} = 2 \cdot \left(b h + h l\right)$

$\text{Base area of prism (Top + Bottom )} = {A}_{b p} = 2 l b$

$\text{Lateral Surface area of cylinder } {A}_{c} = 2 \pi r h$

$\text{Base area of cylinder(Top + Bottom) } {A}_{b c} = 2 \pi {r}^{2}$

$\text{Given : } l = 8 c m , b = 5 c m , h = 4 c m , r = 2 c m$

$\text{L S A of rect. prism } {A}_{l} = 2 \left(8 \cdot 5 + 4 \cdot 8\right) = 144 c {m}^{2}$

$\text{L S A of cylinder } {A}_{c} = 2 \pi \left(\frac{2}{2}\right) \cdot 4 = 8 \pi c {m}^{2}$

$\text{Base areas of rect. prism } = {A}_{b p} = 2 \cdot 8 \cdot 5 = 80 c {m}^{2}$

$\text{Base areas of cylinder } = {A}_{b c} = \pi {2}^{2}$ = 4 pi cm^2

$\text{Total Surface Area of the solid } T S A = {A}_{l} + {A}_{c} + {A}_{b p} - {A}_{b c}$

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