Question

PLZ HELP

Answer 1

Answer:

80πcm²

Please see the attached file for your reference

Step-by-step 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