School

University of the People **We aren't endorsed by this school

Course

CHEM PHYSICAL C

Subject

Mathematics

Date

Nov 3, 2023

Pages

3

Uploaded by MicahelJScott on coursehero.com

BERHAN COMPUTER AND TUTORIAL CLASS
Chapter Iv
1 . If
ABC
Ξ
DEF then
CBA
Ξ
_______
a.
DEF
b.
EDF c.
FDE
d.
FED
e.
none
2.In fig. 1
ABC and
DBC are two isosceles triangles with the same base BC if AD
is extended
to intersect BC at P.
Then which of following is not true
a.
ABD
Ξ
ACD
b.
ABP
Ξ
ACP
c. <BAD
Ξ
<CAD
d.
AP is a perpendicular bisector of BC
e. none
3. In fig. 2
it is given that AB=CF,EF=BD and <AFE Ξ <CBD prove that
AFE Ξ
CB
4. In fig. 4
ABC is isosceles triangle with
AB =AC and E is the midpoint of BC : prove that
AE
BC
5. In fig .4
line segments AB and CD bisect each other at F show that
a. <A Ξ <B
b, AC Ξ DB
6. Prove that the angle bisector of the vertex angle of
An isosceles
triangle is perpendicular at the midpoint of the base.
7.In the fig.5 ABCD is a square. E is the midpoint of CD show that AE ΞBE
8.
In fig. 6
PQR is an equilateral triangle
OR and QL altitudes
prove that OR=QL
9. Prove the following theorems:
a. A point at equal distance from two points is on the perpendicular bisector of the line segment.
b. A point at equal distance from two sides of a triangle is on the angle bisector.
C. A line segment
perpendicular to the base of an isosceles triangle passes through the midpoint.
d. The pairs of opposite side of a parallelogram are equal.
e. The pairs of opposite angles of a parallelogram are equal.
f. The diagonals of a rhombus are perpendicular to each other.
9. In fig.3
ABC if the height corresponding to base BC =8cm find the length of the height
Corresponding to AC:
10. Find the area of the following figures:
11.A plot of land in the shape of an isosceles trapezium (see figure 4) .The area
of the plot is:
12. Two triangles have equal bases. The corresponding height of the one is 5 times that of the
the other. Then the ratio of their areas is:
a. 5:1
b.
10:5
c.25:1
d. 20:5
d. none
13.Which of the following is false?
a.
A rhombus with side 12cm and one angle 150
0
has an area of 72sq.cm.
b.
Two sides of a triangle are 15 and 20 units long. If the altitude to the 15cm side is 8cm
Then the altitude to the 20cm side is 6cm.
c.
The area of a rhombus with diagonals 15 cm and 20 cm is 150sq. cm.
d.
The two regions into which the medians of a triangle separates the triangular region have
Always equal areas.
E. none
14.In fig.3 ABCDEF is a regular hexagon of side 8cm then the area of the
shaded region is.
15. The area of a regular inscribed hexagon is 27√3cm
2
then which one is true?
a. the length of the side of the polygon is 3cm.
b. the radius of the circle is 3 cm
c. the perimeter of the polygon is 15 units.
d. the circumference of the circle is 8 П
e
16 .If r is the radius of a circle inscribed in an equilateral triangle, the area of the triangle is
17.
In fig .4 ABCD is a square of side 3cm.If the radius of the circle with
center E is 1cm and circle B is 2cm. The perimeter of the shaded part is:
19. The lengths of the sides of
DEF are DE=4cm, EF=6cm and DF= 8cm. The length of the
Altitudes
to DE
DF
and EF are?
18.A regular hexagon is inscribed in a circle of radius 6cm .Which of the following is not true?
a.
The area of the hexagon is 48 √3cm
2
b.
The area of the region between the circle and the hexagon is
12( 3П- 4√3)cm
2

BERHAN COMPUTER AND TUTORIAL CLASS
c.
The perimeter of the hexagon is
36cm
d.
Area of the triangle formed by joining
any three
consecutive vertices of the hexagon is 27√3cm
2
e.
none
20.If the hypotenuse of a 30
0
-60
0
-90
0
triangle
is 12cm .which of the following is not true?
a.
The perimeter of the triangle 18+6√3 cm.
b.
The length of the altitude to the hypotenuse is 3√3 cm.
c.
The area of the triangle is 36√3 cm
2
.
d.
The shortest side of the triangle is 6cm
e. none
21. In the fig. 1 AC=10cm and each shaded triangle is an equilateral triangle, then the
total area of the shaded region is:
22. The ratio of the areas of inscribed to circumscribed equilateral triangles in
a circle is:
a.
1: 4
b.
1:3
c. √3: 2
d . 1: 2
e. none
23. In fig. 2
the center of the circle is 0 and the radius of the circle
is 4cm. The area of the shaded region is:
a. 3(П- 2)cm
2
b. 2(П -3) cm
2
c. 4(П - 2) cm
2
d. 2(П - 2) cm
2
e. none
24.Two pieces of wire of equal lengths are bent , one in the shape of a square and the other in the shape of an
equilateral triangle. What is the ratio of the areas of the regions enclosed by each wires is ;
25.Which of the following is not true?
a.
An equilateral triangle inscribed in a circle of area
4 Пcm
2
is 4√3cm
b. If the length of the hypotenuse of a
Right isosceles triangle is x cm
then the length Of its legs is √2x/2cm.
c.
The area of a square inscribed in a
circle of radius
r is 4r
2
.
d. The area of a triangle with sides 25cm, 25cm and 48cm is 168cm
2
.
e. none
26.The sides of triangle are
25cm, 25cm and 48cm a new triangle is formed by joining the mid
points of the sides
of the triangle then the area of the new triangle formed
27.In fig 1, what is the area and perimeter of the shaded part?
28. A cylindrical concrete pipe as shown in fig.2
of 10m length, inside diameter
60cm and outside diameter 65cm is painted at the cost
of Nakfa
7 per
square meter. Find the total cost of
painting the concrete.
a.
27,500nk
b.
2500nk
c. 250nk
d. 275nk
e.
none
29. In the fig.3 In an equilateral
ABC of side length 6cm a new triangle
DEF is
formed by joining the mid points of the sides. Then the ratio of their areas is:
a.
1:2
b. 2:3
c. 1:4
d.1:3
e. none
30.
Find the area and perimeter of the shaded regions of each of the following figures
AB=4cm
31. A girl wishes to sew a cloth as the pattern in fig. 4 .The tip of each petal
is 7cm from the center of the design. Find the area and perimeter
of the design?
32. A regular hexagon ABCDEF is inscribed in a circle of radius Xcm. Then
the area of the shaded
part in terms of X is:
a.
[Π- √3
] x
2
cm
2
b.[ Π- 3√3
] x
2
cm
2
2
2
c. [Π - 3]
x
2
cm
2
d.
[3
- Π] x
2
cm
2
e. none
2
2
33. In fig.4 the center of the semi-circle is O with radius r units
If m(arc BP)=2m(arc PA). Then
Which of the following is true?
a. BP= r
b. AP= √3/3 r
c. the area of the shaded part is
r
2
[Π- 3]
c. the area of
ABP
is 3r
2
/2√3
e. none
2
34. In the fig 5
PQ
=QR=RS. The diameter of the circle is 12cm .then find the area
and perimeter

BERHAN COMPUTER AND TUTORIAL CLASS
of the shaded part
35.Find the area of a sector bounded by an arc of 60
0
in a circle of radius 3√2 cm
36. A swimming pool is 20m in length, 15m in breadth and 4m in depth. Then
the cost of cementing its floor and walls at
a rate of 12Nk per m
2
.
37. The radius of a cone is 5cm and the height is 13cm. Then the volume of the cone is:
a. 65Πcm
3
b.45Πcm
3
c. 60Πcm
3
d. 50Πcm
3
e. none
38. Find the area and perimeter of the shaded parts below
39.The surface area of a cone ,if its slant height is 25cm and the base diameter is 14cm
40.If the lateral surface area of a cone is 4070cm
2
and the diameter is 70cm.
Then the length of the slant height is;
41. In fig .1 the triangular pyramid AB=14cm
AB=11cm and BD=15 cm and
h= √6 cm then the volume of the pyramid is:
42. Find the surface area and volume of a square based pyramid with base length 12cm and
slant height
10cm.
43. Find the volume and surface area of a square based pyramid with base length 10cm
and altitude 12cm.
**44. How many spherical balls of each 4.2cm in diameter can be obtained from rectangular solid of lead with
dimensions
66cm, 42cm ,21cm.( use П= 22/7)
44. If a plane intersect a sphere of diameter 26cm at a distance 12cm from the center. Find the radius of the
circle
formed
45 A metallic spherical balls of radius 3cms is melted and the total substance is utilized
to form some equal balls of each with diameter 0.6cm . The number of these smaller balls is:
46.
Find the volume and surface area of the following solid figures.

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