Geometry Aptitude Questions & Answers
Last Updated :
06 Nov, 2024
Geometry is the study of different varieties of shapes, figures, and sizes. It gives us knowledge about distances, angles, patterns, areas, and volumes of shapes. In this article, we have provided aptitude questions with solutions on geometry along with unsolved questions as well.
Prerequisites:
Aptitude Questions on Geometry
Following are some of the Geometry questions along with their solutions:
Question 1: In a circle with a radius of 10 cm, find the length of a chord that is 6 cm from the center.
Solution:
Let the radius r = 10cm and the distance from the center to the chord d = 6.
Use the formula for the chord length:
L = 2\sqrt{r^2 - d^2}
L = 2\sqrt{10^2 - 6^2}
= 2\sqrt{100 - 36}
= 2√64
= 2 × 8
= 16 cm
Question 2: Find the sum of the interior angles of a polygon with 8 sides.
Solution:
Sum of interior angles of an n-sided polygon = (n−2) × 180∘
Sum = (8 − 2) × 180 = 6 × 180 = 1080∘
Question 3: Find the measure of an angle if five times its complement is 10° less than twice its supplement.
Solution:
According to the problem:
5 × (90∘ − x) = 2 × (180∘ − x) − 10∘
Now, solve the equation:
450∘ − 5x = 360∘ − 2x − 10∘
450∘ − 350∘ = −2x + 5x
100∘ = 3x
x = 33.33∘
Question 4: In a triangle ΔXYZ, if 3∠X = 4∠Y = 5∠Z3, then find the value of ∠X.
Solution:
Let: 3∠X = 4∠Y = 5∠Z = k
From this, we can express the angles as:
- ∠X = k/3
- ∠Y = k/4
- ∠Z = k/5
The sum of the angles in a triangle is 180∘:
∠X + ∠Y+ ∠Z = 180∘
Substituting the expressions for ∠X, ∠Y, and ∠Z:
k/3 + k/4 + k5 = 180∘
20k + 15k + 12k/60 = 180∘
47k = 10800
k = 229.79∘
∠X = k/3 = 229.79/3 = 76.6.
Question 5: What is the formula for calculating the volume of a cylinder, and how do you apply it to a cylinder with a radius of 7 cm and a height of 10 cm?
Solution:
To calculate the volume of a cylinder, you can use the formula:
Volume = πr2h
r = 7
h =10
volume = π(7 × 7) × 10
490π cm3
Question 6: A triangle has sides of lengths 12 cm, 12 cm, and 9 cm. Calculate the area of the triangle.
Solution:
A triangle has a base b=10 and two equal sides of 13 cm each.
Find the height h by splitting the triangle into two right triangles.
h2 = 132 − 52 = 169 − 25 =144
h = 12cm
Calculate the area using the formula: Area = 1/2 × b × h = 1/2 × 10 × 12 = 60 cm2
Thus, the area of the triangle is 60 cm.
Question 7: The distance between the centers of two circles with radii 8 cm and 5 cm is 20 cm. What is the length of the traverse common tangent to the circles?
Solution:
Length of traverse common tangent = √[(Distance between their centres)2-(r1 + r2)2]
= √[(20)2 - (8 + 5)2]
= √(400 - 169)
= √ (231)
= 15.2 cm
Question 8: If each interior angle of a regular polygon is 120∘120^\circ120∘, what is the number of sides of the polygon?
Solution:
Interior angle = 140∘
Exterior angle = 180∘ − 140∘ = 40∘
Number of sides of polygon = 360∘/exterior angle = 360∘/40∘ = 9
The number of sides of the polygon is 9.
Practice Questions on Geometry Aptitude
1. In a circle of radius 15 cm, find the length of a chord that is 9 cm from the center.
2. Find the sum of the interior angles of a polygon with 10 sides.
3. Find the measure of an angle if four times its complement is 20° less than three times its supplement.
4. The angles of a triangle are in the ratio of 4:5:6. Find the largest angle of the triangle.
5. What is the formula for calculating the volume of a cone, and how do you apply it to a cone with a radius of 5 cm and a height of 12 cm?
6. A triangle has sides of lengths 5 cm, 5 cm, and 6 cm. Calculate the area of the triangle.
7. The distance between the centers of two circles with radii 7 cm and 3 cm is 18 cm. What is the length of the traverse common tangent to the circles?
8. If each interior angle of a regular polygon is 135∘, what is the number of sides of the polygon?
Answer Key
- Length of the chord: 24 cm
- The sum of the interior angles: 1440°
- Measure of the angle: 160°
- Largest angle of the triangle: 72∘
- The volume of the cone: 100π cm³
- Area of the triangle: 12 cm²
- Length of the traverse common tangent: 15 cm
- Number of sides of the polygon: 8
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