Master 3D Shapes: Geometry for Healthcare Professionals

Question 1

Which transformation involves flipping a 3D shape over a plane?

Accepted Answer

Reflection

Answer

Rotation

Answer

Translation

Answer

Dilation

Question 2

Which of the following is a defining trait of a prism?

Accepted Answer

All of the上述

Answer

It possesses two parallel bases.

Answer

Its lateral faces are parallelograms.

Answer

Its cross-sections are triangular.

Question 3

Which transformation can alter the volume of a 3D shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Question 4

A cube has a side length of 5 cm. What is its volume?

Accepted Answer

125 cm³

Answer

25 cm³

Answer

250 cm³

Answer

625 cm³

Question 5

A cuboid has length 10 cm, width 5 cm, and height 3 cm. What is its surface area?

Accepted Answer

150 cm²

Answer

90 cm²

Answer

120 cm²

Answer

240 cm²

Question 6

What is the cross-section of a cylinder?

Accepted Answer

Circle

Answer

Square

Answer

Rectangle

Answer

Triangle

Question 7

A cuboid with dimensions 5 cm x 3 cm x 2 cm undergoes a transformation that doubles its length and width. Determine the new volume of the cuboid.

Accepted Answer

96 cm³

Answer

12 cm³

Answer

24 cm³

Answer

48 cm³

Question 8

What is the volume formula for a cone with radius 'r' and height 'h'?

Accepted Answer

⅓πr²h

Answer

πr²h

Answer

⅔πr²h

Answer

4/3πr²h

Question 9

Identify the characteristic of a regular octahedron.

Accepted Answer

8 faces, all equilateral triangles

Answer

6 faces, all squares

Answer

12 edges, all equal in length

Answer

8 vertices, all connected by 3 edges

Question 10

A cuboid has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is its surface area?

Accepted Answer

106 cm²

Answer

94 cm²

Answer

118 cm²

Answer

130 cm²

Question 11

A cone has a radius of 5 cm and a height of 10 cm. What is its volume?

Accepted Answer

83.78 cm³ (approximately)

Answer

167.55 cm³ (approximately)

Answer

335.10 cm³ (approximately)

Answer

670.21 cm³ (approximately)

Question 12

A cube is translated 5 units to the right along the x-axis. What are the coordinates of its new centre?

Accepted Answer

(5, 0, 0)

Answer

(0, 5, 0)

Answer

(0, 0, 5)

Answer

(5, 5, 0)

Question 13

A cube has a side length of 'x' cm. Express its volume in terms of 'x'.

Accepted Answer

x² cm³

Answer

x cm³

Answer

2x³ cm³

Answer

3x⁴ cm³

Question 14

Calculate the volume of a cube with side length 'a'.

Accepted Answer

a³

Answer

2a³

Answer

4a³

Answer

6a³

Question 15

Determine the surface area of a cuboid with length 'l', width 'w', and height 'h'.

Accepted Answer

2(lw + wh + hl)

Answer

lw + wh + hl

Answer

4(lw + wh + hl)

Answer

lwh

Question 16

Which transformation moves an object from one point to another without changing its size or shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 17

Calculate the slant height of a cone with radius 'r' and height 'h'.

Accepted Answer

√(r² + h²)

Answer

r + h

Answer

r - h

Answer

h - r

Question 18

Calculate the volume of a pyramid with a square base of side length 'a' and height 'h'.

Accepted Answer

(1/3)a²h

Answer

(1/2)a²h

Answer

a²h

Answer

2a²h

Question 19

Find the surface area of a sphere with radius 'r'.

Accepted Answer

4πr²

Answer

4πr³

Answer

πr²

Answer

2πr³

Question 20

Calculate the volume of a rectangular prism with dimensions: length 4 cm, width 3 cm, and height 2 cm.

Accepted Answer

24 cm³

Answer

36 cm³

Answer

48 cm³

Answer

12 cm³

Question 21

What is the volume of a cube with sides of length 5 centimeters?

Accepted Answer

125 cm³

Answer

100 cm³

Answer

50 cm³

Answer

25 cm³

Question 22

Which of the following is NOT a formula for calculating the surface area of a cuboid?

Accepted Answer

2(l + w + h)

Answer

lwh

Answer

lw + lh + wh

Answer

2(lw + lh + wh)

Question 23

A cone has a radius of 4 centimeters and a height of 6 centimeters. What is its volume?

Accepted Answer

32π cm³

Answer

12π cm³

Answer

64π cm³

Answer

16π cm³

Question 24

Which of the following transformations does NOT preserve the shape of a 3D figure?

Accepted Answer

Shear

Answer

Reflection

Answer

Translation

Answer

Rotation

Question 25

A sphere has a diameter of 10 centimeters. What is its surface area?

Accepted Answer

100π cm²

Answer

25π cm²

Answer

125π cm²

Answer

50π cm²

Question 26

Which of the following is a property of a regular tetrahedron?

Accepted Answer

All faces are congruent equilateral triangles.

Answer

All faces are congruent squares.

Answer

All faces are congruent hexagons.

Answer

All faces are congruent pentagons.

Question 27

A cylinder has a radius of 3 centimeters and a height of 5 centimeters. What is its volume?

Accepted Answer

45π cm³

Answer

30π cm³

Answer

60π cm³

Answer

15π cm³

Question 28

Which of the following solids has the greatest volume?

Accepted Answer

Cone with radius 5 cm and height 10 cm

Answer

Cylinder with radius 5 cm and height 5 cm

Answer

Cube with side length 5 cm

Answer

Sphere with radius 5 cm

Question 29

A prism has a square base with side length 4 centimeters and a height of 6 centimeters. What is its surface area?

Accepted Answer

104 cm²

Answer

80 cm²

Answer

48 cm²

Question 30

Which of the following nets can be folded to form a cube?

Accepted Answer

A square with 4 equal flaps attached to each side.

Answer

A triangle with 4 equal flaps attached to each side.

Answer

A rectangle with 2 equal flaps attached to the long sides.

Answer

A pentagon with 5 equal flaps attached to each side.

Question 31

Calculate the volume of a cube with a side length of 5 cm.

Accepted Answer

125 cm³

Answer

25 cm³

Answer

65 cm³

Answer

50 cm³

Question 32

Out of a sphere, cuboid, cube, and cone, which shape generally has the largest surface area?

Accepted Answer

Sphere

Answer

Cube

Answer

Cuboid

Answer

Cone

Question 33

A sphere has a volume of 36π cm³. What is its radius?

Accepted Answer

3 cm

Answer

12 cm

Answer

9 cm

Answer

6 cm

Question 34

Which of these transformations produces a congruent image of a 3D shape: Rotation, Translation, Dilation, or Reflection?

Accepted Answer

Rotation

Answer

Translation

Answer

Dilation

Answer

Reflection

Question 35

A cone has a radius of 5 cm and a slant height of 13 cm. Calculate its height.

Accepted Answer

12 cm

Answer

6 cm

Answer

24 cm

Answer

10 cm

Question 36

What is the formula for calculating the surface area of a cuboid with length (l), width (w), and height (h)?

Accepted Answer

2(lw + lh + hw)

Answer

4/3πr³

Answer

a²

Answer

πr²

Question 37

A cylinder has a radius of 3 cm and a height of 6 cm. Find its volume.

Accepted Answer

54π cm³

Answer

9π cm³

Answer

18π cm³

Answer

36π cm³

Question 38

Which of the following is NOT a property of a regular tetrahedron: All edges are equal, All faces are congruent equilateral triangles, Has 4 faces and 4 vertices, All vertices are equidistant from each other?

Accepted Answer

All edges are equal

Answer

Has 4 faces and 4 vertices

Answer

All vertices are equidistant from each other

Answer

All faces are congruent equilateral triangles

Question 39

Calculate the surface area of a sphere with a diameter of 10 cm.

Accepted Answer

100π cm²

Answer

200π cm²

Answer

25π cm²

Answer

50π cm²

Question 40

Which of these transformations does NOT change the volume of a 3D shape: Translation, Rotation, Dilation, or Reflection?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation