From a cylindrical piece of wood of radius hcm and height 5cm a right circular come with same base radius and height 3cm is carved out. What is the total surface area of the remaining wood?
Answers
The remaining part comprises of the complete lateral outer part of cylinder, with one base and the additional surface created because of the cut out cone, which is periphery of the hollow created. The slant height, l of the cone would be :
[math]l = \sqrt{3^2 + 4^2} = 5[/math]
So, the total area would be the sum of area of one base of cylinder, lateral surface area of cylinder and lateral surface area of the cone, which would be:
[math]S = \pi * 4^2 + 2\pi * 4 * 5 + \pi * 4 * 5 = 76\pi[/math]
P.S. Formulae for the three parts
Area of base of cylinder, [math]A = \pi r^2[/math], where r is the radius of base
Lateral area of cylinder, [math]A = 2\pi rh[/math], where h is the height of cylinder
Lateral area of cone, [math]A = \pi rl[/math], where l is the slant height that we computed above
Slant height of cone, [math]l = \sqrt{r^2 + h^2}[/math], where h is the height of cone.