Question
Complete the following table and verify Euler’s formula in each case.
 
 
Faces (F)
6
4
9
7
Edges (E)
12
6
16
15
Vertex (V)
8
4
9
10

Answer

 
I
II
III
IV
Faces (F)
6
4
9
7
Edges (E)
12
6
16
15
Vertices (V)
8
4
9
10
Euler's formula ( F - E + V)
6 - 12 + 8 = 2
4 - 6 + 4 = 2
9 - 16 + 9 = 2
7 - 15 + 10 = 2
Hence Euler's formula is verified for these figures.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Find the area of a rhombus having each side equal to 13 cm and one of the diagonals equal to 24 cm .
Simplify:
$\Big(\frac{-9}{4}\times\frac{5}{3}\Big)+\Big(\frac{13}{2}\times\frac{5}{6}\Big)$
Find the area of a rhombus each side of which measures 20cm and one of whose diagoanls is 24cm.
Students of a certain school went for a picnic to a farm by bus. Here are some of their experiences. Say whether the quantities in each are in direct or in inverse proportion.

i. Each student paid Rs 60 for the expenses.
As there were 45 students,___rupees were collected.
Had there been 50 students,___rupees would have been collected.
The number of students and money collected are in___proportion.

ii. The sweets shop near the school gave 90 laddoos for the picnic.
If 45 students go for the picnic, each will get___laddoos.
If 30 students go for the picnic, each will get___laddoos.
The number of students and that of laddoos each one gets are in___proportion.

iii. The farm is 120 km away from the school.
The bus went to the farm at a speed of 40 km per hour and took___hours.
On the return trip, the speed was 60 km per hour. Therefore, it took___hours.
The speed of the bus and the time it takes are in___proportion.

iv. The farmer picked 180 bors from his trees.
He gave them equally to 45 students. Each student got___bors.
Had there been 60 students, each would have got___bors.
The number of students and the number of bors each one gets are in___proportion.

A horse is tied to a pole in a park with a string 21m long. Find the area over which the horse can graze.
A tricycle is sold at a gain of 15%. Had it been sold for Rs. 108 more, the profit would have been 20%. Find its cost price.
$\text{x}+\frac12=\frac72$
Two parallel lines I and $m$ are cut by a transversal $t$. If the interior angles of the same side of $t$ be $(2 x-8)^{\circ}$ and $(3 x-7)^{\circ}$, find the measure of each of these angles.
Simplify:
$(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x+y)$
The radius of one circluar field is 20m and that of another is 48m. Find the radius of the third circular field whose area is equal to the sum of the areas of two fields.