Geometry questions, with answers, are provided for students to help them understand the topic more easily. Geometry is a chapter that has been included in almost all classes. The questions will be provided in accordance with NCERT guidelines. The use of geometry can be seen in both mathematics and everyday life. Thus, the fundamentals of this topic must be understood. The questions here will cover both the fundamentals and more difficult problems for students of all levels. As a result, students will be skilled in using it to solve geometry problems. Click here to learn more about Geometry.
| Definition: Geometry is a discipline of mathematics dealing with the study of various forms of shapes and sizes of real-world objects. We study different angles, transformations, and similarities of figures in geometry. The fundamentals of geometry are based on the concepts of point, line, angle, and plane. These fundamental geometrical concepts govern all geometrical shapes. |
Here, we are going to discuss different geometry questions, based on different concepts with solutions.
Geometry Questions with Solutions
1. The lines that are equidistant from each other and never meet are called ____.
Solution:
Parallel lines are the lines that are equidistant from each other and never meet. The parallel lines are represented with a pair of vertical lines and its symbol is “||”. If AB and CD are the two parallel lines, it is denoted as AB || CD.
2. If two or more points lie on the same line, they are called _____.
Solution:
If two or more points lie on the same line, they are called collinear points. If points A, B and C lie on the same line “l”, then we can say that the points are collinear.
| Angles: An angle is defined as the shape created by two rays intersecting at a common endpoint. The symbol is used to symbolise an angle is “∠” and it is measured in degrees (°).
Angles can be categorized based on their measurements. They are: Acute Angle: Angle < 90° Right Angle: Angle = 90° Obtuse Angle: Angle > 90° Straight Angle: Angle = 180° Reflex Angle: Angle > 180° and < 360° Complete Angle: Angle = 360° |
3. Find the number of angles in the following figure.
Solution:
In the given figure, there are three individual angles, (i.e.) 30°, 20° and 40°.
Two angles in a pair of 2. (i.e.) 20° + 30° = 50° and 20 + 40 = 60°
One angle in a pair of 3 (i.e) 20° + 30° + 40° = 90°
Hence, the total number of possible angles in the given figure is 6.
4. In the given figure, ∠BAC = 90°, and AD is perpendicular to BC. Find the number of right triangles in the given figure.
Solution:
Given: ∠BAC = 90° and AD⊥BC.
Since AD⊥BC, the two possible right triangles obtained are ∠ADB and ∠ADC.
Hence, the number of right triangles in the given figure is 3.
I.e., ∠BAC = ∠ADB = ∠ADC = 90°.
| Two Dimensional Shapes: A two-dimensional shape can be characterised as a flat planar figure or a shape that has two dimensions — length and width. There is no thickness to two-dimensional shapes. Circles, triangles, squares, rectangles, and other 2D shapes are examples.
The region enclosed by the figure is the area of a 2D shape. The perimeter of a two-dimensional shape is equal to the sum of the lengths of all its sides. Also read: Area and Perimeter Formulas. |
5. The length of a rectangle is 3 more inches than its breadth. The area of the rectangle is 40 in2. What is the perimeter of the rectangle?
Solution:
Given: Area = 40 in2.
Let “l” be the length and “b” be the breadth of the rectangle.
According to the given question,
b = b and l = 3+b
We know that the area of a rectangle is lb units.
So, 40 = (3+b)b
40 = 3b +b2
This can be written as b2+3b-40 = 0
On factoring the above equation, we get b= 5 and b= -8.
Since the value of length cannot be negative, we have b = 5 inches.
Substitute b = 5 in l = 3 + b, we get
l = 3 + 5 = 8 inches.
As we know, the perimeter of a rectangle is 2(l+b) units
P = 2 ( 8 + 5)
P = 2 (13) = 26
Hence, the perimeter of a rectangle is 26 inches.
6. What is the area of a circle in terms of π, whose diameter is 16 cm?
Solution:
Given: Diameter = 16 cm.
Hence, Radius, r = 8 cm
We know that the area of a circle = πr2 square units.
Now, substitute r = 8 cm in the formula, we get
A = π(8)2 cm2
A = 64π cm2
Hence, the area of a circle whose diameter is 16 cm = 64π cm2.
7. Find the missing angle in the given figure.
Solution:
Given two angles are 35° and 95°.
Let the unknown angle be “x”.
We know that sum of angles of a triangle is 180°
Therefore, 35°+95°+x = 180°
130°+ x = 180°
x = 180° – 130°
x = 50°
Hence, the missing angle is 50°.
| Three Dimensional Shapes: Solids with three dimensions, such as length, breadth, and height, are known as 3D forms. Cube, cuboid, cylinder, cone, sphere, and other 3D shapes are examples.
Surface area and volume are two properties of 3D geometric shapes. The area covered by the 3D shape at the base, top, and all faces, including any curved surfaces, is referred to as the surface area. The volume is defined as the total amount of space required for the 3D shape. Also read: Surface Area and Volume Formulas. |
8. Find the curved surface area of a hemisphere whose radius is 14 cm.
Solution:
Given: Radius = 14 cm.
As we know, the curved surface area of a hemisphere is 2πr2 square units.
CSA of hemisphere = 2×(22/7)×14×14
CSA = 2×22×2×14
CSA = 1232
Hence, the curved surface area of a hemisphere is 1232 cm2.
9. Find the volume of a cone in terms π, whose radius is 3 cm and height is 4 cm.
Solution:
Given: Radius = 3 cm
Height = 4 cm
We know that the formula to find the volume of a cone is V = (⅓)πr2h cubic units.
Now, substitute the values in the formula, we get
V = (⅓)π(3)2(4)
V = π(3)(4)
V = 12π cm3
Hence, the volume of a cone in terms of π is 12π cm3.
10. The base area of a cylinder is 154 cm2 and height is 5 cm. Find the volume of a cylinder.
Solution:
Given: Base area of a cylinder = 154 cm2.
As the base area of a cylinder is a circle, we can write πr2 = 154cm2.
We know that the volume of a cylinder is πr2h cubic units.
V = 154(5) cm3
V = 770 cm3
Hence, the volume of a cylinder is 770 cm2.
Practice Questions
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- Find the area of a square whose side length is 6 cm.
- Find the number of obtuse angles in the given figure.
3. Find the number of line segments in the given figure and name them.
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