Question

PLZ HELP

A piece of wood is designed in the shape of a cone

A cylindrical hole of radius 4cm and depth 2 cm has been drilled into the base,

The surface area of the piece of wood has to be painted, except for the area inside the hole.

work out the surface area to be painted

give your answer in terms of pi, thank you sooo much

Answer 1

80πcm²

Please see the attached file for your reference

Explanation:

This problem bothers on the mensuration of solid shapes, a cone

The total surface area of cone is the sum of the curved surface area and the base surface area

Curved surface area = πrl

Base area = πr²

From the figure

The surface area to be painted is

Base area - area of hole

Given diameter of base = 12cm

Radius of base = 12/2= 6cm

Area of base = π(6²)

Area of base = 36πcm²

Area of hole =πr²

Given radius of hole = 4cm

Area =π(4²)

Area = 16πcm²

Hence area to be painted at the base is 36πcm²- 16πcm²

Area to be painted at base 20πcm²

For the curved surface area

Area = πrl

Sine the base radius is 6cm

Given height h= 8cm

We need to find the slant height l

Since the slant height the height and the radius of a cone forms a right triangle

Applying Pythagoras theorem

l= √r²+h²

l= √6²+8²

l=√36+64

l=√100

l= 10cm

We can now solve for the curved surface area

A=πrl

A= π*6*10

A= 60πcm²

Hence the total surface area to be painted is 60πcm² +20πcm²

80πcm²