3. Can a polyhedron have 10 faces , 22 edges and 14 vertices?
SECTION - B
4. The perimeter of a trapezium is 104 m. Its non - parallel sides are 18 m and 22 m
and its altitude is 16 m. Find the area of a trapezium.
5.If the weight of 15 sheets of thick paper is 75 gram , how many sheets of the same
paper would weigh 3 kilogram.
6. The length, breadth and height of a cuboid are in the ratio 3:2:1. If its volume is 162
cm, find its total surface area.
SECTION - C
7.The volume of a metallic cylindrical pipe is 748 cm°. Its length is 14 cm and its
external radius is 9 cm. Find its thickness.
8. Find the value of p and q in the following table, if x and y vary directly.
Х 5
р
10
у
8
32 9
Answers
Answer:
3. No a polyhedron can't have 10 faces , 20 edges, and 15 vertices as eulers formula is not satisfied
Euler's formula = faces + vertices -edges = 2
10 + 15 - 20 = 2
25 - 20 = 2
5 2
So, it can't have 10 faces , 20 edges, and 15 vertices.
4. Perimeter of Trapezium = 104 m
Non parallel sides are 22 m and 18 m
Let X and Y be the parallel sides of trapezium.
Altitude = 16 m
Perimeter of trapezium = X + Y + 22 + 18
104 = X + Y + 40
X+Y = 104-40
X + Y = 64
Area of trapezium = 1/2 ( sum of parallel side)× altitude
=1/2 (X+Y) × 16
=(1/2) 64 × 16
=512 m²
Therefore Area of Trapezium is 512m².
5. Weight of 15 sheets of paper = 75 grams
weight of 1 sheet of paper = 75/15 = 5 gm
3 kg = 3000gm
So, number of sheets of paper weigh 3000 gm = 3000/5 = 600
6. Volume = l × b × h
162 = 3x × 2x × 1x
162 = 6x³
162/6 = x³
27 = x³
x = 3
l = 9cm , b = 6cm, h = 3cm
TSA = 2 (lb + bh + hl)
= 2 (54 + 18 + 27)
= 2 (99)
= 198 cm²
