Geometry Quizzes: Test Your Knowledge of Shapes, Angles, and More

Question 1

What is the formula for calculating the volume of a cone?

Accepted Answer

V = (1/3) * πr²h

Answer

V = πr²h

Answer

V = (4/3) * πr³

Answer

V = (1/2) * πr²h

Question 2

Find the volume of a rectangular prism with a length of 10 centimeters, a width of 5 centimeters, and a height of 3 centimeters.

Accepted Answer

150 cubic centimeters

Answer

15 cubic centimeters

Answer

250 cubic centimeters

Answer

300 cubic centimeters

Question 3

To calculate the area of a triangle, which of these formulas should you use?

Accepted Answer

A = (1/2)bh

Answer

A = lw

Answer

A = πr²

Answer

A = 4/3πr³

Question 4

What is the formula for calculating the circumference of a circle?

Accepted Answer

$ 2 pi r$

Answer

$ pi r^2$

Answer

$ 4 pi r$

Answer

$ r^2$

Question 5

What is the formula for calculating the area of a triangle?

Accepted Answer

A = ½ * b * h

Answer

A = 4 * s

Answer

A = π * r^2

Answer

A = l * w

Question 6

Which of the following is NOT a property of a square?

Accepted Answer

Has obtuse angles

Answer

Has four right angles

Answer

Has four equal sides

Answer

Is a regular polygon

Question 7

Calculate the area of a triangle with a base of 10 cm and a height of 8 cm.

Accepted Answer

40 cm²

Answer

20 cm²

Answer

80 cm²

Question 8

Identify the condition for two triangles to be considered similar.

Accepted Answer

Corresponding angles that are congruent

Answer

The same area

Answer

Equal side lengths

Answer

None of the above

Question 9

Determine the measure of the interior angle of a regular hexagon.

Accepted Answer

120 degrees

Answer

150 degrees

Answer

180 degrees

Answer

90 degrees

Question 10

Which of the following is NOT a trigonometric ratio?

Accepted Answer

Area

Answer

Tangent

Answer

Cosine

Answer

Sine

Question 11

State the Pythagorean theorem.

Accepted Answer

a² + b² = c²

Answer

a - b = c

Answer

a + b = c

Question 12

What is the formula for the area of a circle?

Accepted Answer

A = πr²

Answer

A = πr

Answer

A = 2πr

Answer

A = 4πr

Question 13

What is the sum of the interior angles of a triangle?

Accepted Answer

180 degrees

Answer

360 degrees

Answer

90 degrees

Answer

270 degrees

Question 14

Which of the following is NOT a type of quadrilateral?

Accepted Answer

Octagon

Answer

Rectangle

Answer

Trapezoid

Answer

Square

Question 15

What is the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a/b = c

Answer

a - b = c

Answer

πr² = a

Question 16

What is the difference between a regular and irregular polygon?

Accepted Answer

Regular polygons have congruent sides and angles, while irregular polygons do not.

Answer

Irregular polygons are always convex.

Answer

Regular polygons have more sides than irregular polygons.

Question 17

What is the formula for the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = πr²

Answer

C = r/π

Answer

C = 4πr

Question 18

Which of the following is an example of a 3-dimensional shape?

Accepted Answer

Cube

Answer

Line

Answer

Triangle

Answer

Circle

Question 19

What is the name of the point where all the sides of a polygon intersect?

Accepted Answer

Vertex

Answer

Edge

Answer

Midpoint

Answer

Center

Question 20

A triangle with two equal sides and two equal angles is called a(n):

Accepted Answer

Isosceles triangle

Answer

Right triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Question 21

What is the sum of the interior angles of a hexagon?

Accepted Answer

720 degrees

Answer

360 degrees

Answer

540 degrees

Answer

900 degrees

Question 22

A square with sides of length 5 cm has an area of:

Accepted Answer

25 cm²

Answer

100 cm²

Answer

10 cm²

Answer

50 cm²

Question 23

Two triangles are congruent if they have:

Accepted Answer

All corresponding sides and angles equal

Answer

Only corresponding angles equal

Answer

Two corresponding angles and one corresponding side equal

Answer

Two corresponding sides and one corresponding angle equal

Question 24

The diagonal of a square with side length 's' is:

Accepted Answer

√2 * s

Answer

s²

Answer

s

Answer

2 * s

Question 25

Which of the following is NOT a property of a circle?

Accepted Answer

Number of sides

Answer

Diameter

Answer

Radius

Answer

Circumference

Question 26

What is the area of a square with a side length of 5 cm?

Accepted Answer

25 cm²

Answer

15 cm²

Answer

50 cm²

Answer

10 cm²

Question 27

Which of the following angles is an acute angle?

Accepted Answer

30°

Answer

180°

Answer

90°

Answer

120°

Question 28

The Pythagorean theorem states that:

Accepted Answer

a² + b² = c²

Answer

a - b = c

Answer

a / b = c

Answer

a x b = c

Question 29

What is the sum of the interior angles of a hexagon?

Accepted Answer

720°

Answer

540°

Answer

360°

Answer

900°

Question 30

Which of the following shapes is three-dimensional?

Accepted Answer

Cone

Answer

Square

Answer

Line

Answer

Circle

Question 31

What is the line called that divides a circle into two equal halves?

Accepted Answer

Diameter

Answer

Radius

Answer

Tangent

Answer

Chord

Question 32

Which of these is a defining property of a rectangle?

Accepted Answer

Opposite sides are parallel and equal in length

Answer

Opposite angles are equal

Answer

Diagonals bisect each other

Answer

All sides are equal in length

Question 33

Calculate the area of a triangle with a base of 6 cm and a height of 4 cm.

Accepted Answer

12 cm²

Answer

36 cm²

Answer

24 cm²

Answer

6 cm²

Question 34

What type of angle measures more than 90 degrees but less than 180 degrees?

Accepted Answer

Obtuse angle

Answer

Right angle

Answer

Acute angle

Answer

Reflex angle

Question 35

A cube has sides of 5 cm. What is its volume?

Accepted Answer

125 cm³

Answer

312.5 cm³

Answer

65 cm³

Answer

250 cm³

Question 36

Which transformation creates a similar figure but not necessarily congruent?

Accepted Answer

Scaling

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 37

What is the measure of each interior angle in a regular hexagon?

Accepted Answer

120 degrees

Answer

180 degrees

Answer

240 degrees

Answer

60 degrees

Question 38

In a right triangle, which trigonometric ratio represents the length of the adjacent side divided by the hypotenuse?

Accepted Answer

Cosine

Answer

Tangent

Answer

Sine

Answer

Secant

Question 39

What does the Pythagorean theorem state?

Accepted Answer

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

Answer

In a right triangle, the area is equal to half the product of the lengths of the other two sides

Question 40

Which three-dimensional shape has two circular faces and a curved surface connecting them?

Accepted Answer

Cylinder

Answer

Cube

Answer

Cone

Answer

Sphere

Question 41

What is the formula to calculate the surface area of a rectangular prism with length (l), width (w), and height (h)?

Accepted Answer

2(lw + lh + wh)

Answer

lw + lh + wh

Answer

lwh

Answer

2lw + 2lh

Question 42

A rectangular garden is 10 meters long and 5 meters wide. What is its perimeter?

Accepted Answer

30 meters

Answer

15 meters

Answer

25 meters

Answer

50 meters

Question 43

What is the area of a triangle with a base of 8 cm and a height of 6 cm?

Accepted Answer

24 cm²

Answer

12 cm²

Answer

48 cm²

Answer

14 cm²

Question 44

A circle has a diameter of 10 cm. What is its circumference (rounded to the nearest tenth)?

Accepted Answer

31.4 cm

Answer

62.8 cm

Answer

100 cm

Answer

15.7 cm

Question 45

Two triangles are considered congruent if they have:

Accepted Answer

All corresponding sides and angles equal

Answer

One corresponding side and one corresponding angle equal

Answer

Two corresponding sides and one corresponding angle equal

Answer

Two corresponding angles equal

Question 46

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm. What is its volume?

Accepted Answer

60 cm³

Answer

22 cm³

Answer

30 cm³

Answer

12 cm³

Question 47

In a right-angled triangle, the side opposite the right angle is called the:

Accepted Answer

Hypotenuse

Answer

Base

Answer

Altitude

Answer

Perpendicular

Question 48

Two triangles are similar if they have:

Accepted Answer

All corresponding angles equal

Answer

All corresponding sides equal

Answer

One corresponding angle and one corresponding side equal

Answer

Two corresponding sides equal

Question 49

What is the value of sin(30°)?

Accepted Answer

1/2

Answer

√2/2

Answer

1

Answer

√3/2

Question 50

A square has a side length of 7 cm. What is its diagonal length?

Accepted Answer

7√2 cm

Answer

7 cm

Answer

14 cm

Answer

49 cm

Question 51

A cylinder has a radius of 5 cm and a height of 10 cm. What is its surface area?

Accepted Answer

314 cm² (approximately)

Answer

628 cm² (approximately)

Answer

500 cm²

Answer

157 cm² (approximately)