Q1 13 points are marked on the circumference of a circle such that the distance between consecutive points are equal. If lines are drawn from each point to all other points, how many chords would be formed?
72
78
102
108
Q2 What is the ratio of the area of the purple triangle to the red region, if both the vertical and horizontal lines are perpendicular and divide the square into equal parts?
1:4
2:3
1:3
3:5
Q3 How many identical metal cones should be melted to form a cylinder that has twice the radius and twice the height of one of those cones?
4
8
12
24
Answers
Answer:
answer 1 : In the language of geometry, a circle is the locus of points in a plane that are all at an equal distance from a single point, called the center of the circle. The fixed distance is called the radius of the circle.
answer 2 : The area of a scalene triangle with base b and height h is given by 1/2 bh. If you know the lengths of all three sides, you can calculate area using Heron's Formula without having to find the height.
answer 3 : Let R be the radius and H be the height of the cylinder and let rand h be the radius and height of the cone respectively. Then,
3r=2R
and H:h=4:3 ......(i)
⇒
h
H
=
3
4
⇒3H=4h .......(ii)
Let n be the required number of cones which can be made from the materials of the cylinder. Then, the volume of the cylinder will be equal to the sum of the volumes of n cones. Hence, we have
πR
2
H=
3
n
πr
2
h
⇒3R
2
H=nr
2
h
⇒n=
r
2
H
3R
2
H
=
r
2
h
3×
4
9r
2
×
3
4h
[∵ From (i) and (ii), R=
2
3r
and H=
3
4h
]
⇒n=
3×4
3×9×4
⇒n=9