Question

A piece of wood is designed in the shape of a cone. A cylindrical hole of radius 4cm and 2cm has been drilled into the base. The surface area of the piece of wood has to be painted, except from the area inside the hole work out the surface area to be painted give your answer in the terms of pi thank you

Answer 1

Answer:

= 80πcm²

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

Given the information:

• Diameter of base = 12cm => its radius is: 6 cm
• Radius of hole = 4cm
• The height: 8 cm

=> Area of base = π(6²) = 36π cm²

=> Area of the hole = πr² = π(4²) = 16πcm²

As we know that, the surface area of the piece of wood has to be painted at base:

= Base area - area of hole

= 36π cm² - 16πcm²  

= 20πcm²

For the curved surface area can be determined by the following formula:

Area = πrl where l is the slant height

Applying Pythagoras theorem, we have:

$l^{2} = r^{2} + h^{2}$

<=> $l^{2} = 6^{2} + 8^{2}$

<=> $l^{2} =100$

<=> l =10

=> the curved surface area is: π*6*10 =60πcm²

Hence the total surface area to be painted is

= the curved surface area + he surface area of the piece of wood has to be painted at base

=  60πcm² +20πcm²

= 80πcm²

Hope it will find you well.