Question

Answer the following questions.

(a) Find the number of edges of a polyhedron having 20 faces and 12 vertices.

(b) Find the surface area of a cube whose volume is 729 m.​

Answer 1

Answer:

a: According to the formula given by Euler.

F + V = E + 2

Where,

F = no. of faces

V = no. of vertices

E = no. of edges

So,

{F + V = E + 2}}F+V=E+2

=> 20 + 12 = E + 2

=> 32 = E + 2

=> E = 32 - 2

=> E = 30

Therefore, there are 30 edges of a polyhedron having 20 faces and 12 verticles

b: Volume of cube = Side^3Side3

Since we are given that the volume of cube =729 cm^3729cm3

So,  729=Side^3729=Side3

[3]{729} =Side3729=Side

9 =Side9=Side

Thus the side of the given cube is 9 cm

Total Surface area of cube = 6x^26x2

Where x is the side

So, Total Surface area of cube = 6(9)^26(9)2

                                                   = 486 cm^2486cm2

Hence the surface area of the given cube is 486 sq.cm.

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Answer 2

Answer :

1.

Using Euclear 's formula

F +V = E +2

20 + 12 = E+2

32 - 2 = E

E = 30

2. Volume of cube = ( side )^3

$side = 3 \sqrt{729}$

side = 9 m

surface area of cube = 6 ×(side)^2

6 × (9m)^2

6×81 m ^2

486m^2

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