Question

A cone of radius 3cm and slant height 6cm is cut into four identical pieces

Answer 1

The cone has a surface area of A = pi*r*l + pi*r² = 27pi cm². The height of the cone is sqrt(6² - 3²) = 5.196. The cut surfaces are triangles of area 7.794 cm² for a total cut area of 62.354 cm².

27pi + 62.354 = 147.18 cm² or about 147 cm²

Answer 2

Answer:

≈ 147 cm^2   (3 significant digits)

Step-by-step explanation:

To get four identical pieces, the cone must be cut by  two perpendicular planes, through the axis of the cone.

There are three areas to calculate for each piece:

the curved region;  the  base;  and two vertical faces

The height of the cone,  h cm,  is got using Pythagoras on a vertical face:

h^2 = 6^2 - 3^2 = 27;

so  h = 3√3

The whole curved area,  A1 cm^2,  of the four pieces, is given by

A1 = π * 3 * 6, = 18 π

The whole base of the cone,  A2 cm^2, is given by

A2 = π * 3^2 = 9π

With  A3 cm^2  the area of the eight vertical faces,

A3 = 8 * (1/2) * 3 * 3√3 = 36√3

So the total area is  (A1 + A2 + A3) cm^2

                            = (27π + 36√3) cm^2

                            = 147.18 cm^2

                            ≈ 147 cm^2   (3 significant digits)