Geometry of Shapes, Surface Area and Volume - MYP Questionbank | RevisionDojo

Geometry of Shapes, Surface Area and Volume - MYP Questionbank | RevisionDojo

Practice Geometry of Shapes, Surface Area and Volume with authentic MYP MYP Standard Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

A triangle has vertices at $(1, 2)$ , $(3, 2)$ , and $(1, 5)$ . If the triangle is reflected in the line $y = x$ , what are the coordinates of the vertices of the image triangle?

Question 2

A dilation is centered at the origin with a scale factor of $k = -0.5$ . If the pre-image is a line segment of length $10$ units, what is the length of the image segment and where is it located relative to the center?

Question 3

A small soil sample has a volume of $0.002 \text{ m}^3$ . How many cubic millimeters ( $\text{mm}^3$ ) is this volume?

Question 4

In a right cone, which equation correctly relates the radius $r$ , the vertical height $h$ , and the slant height $s$ ?

Question 5

A triangle with vertices at $(2, 2)$ , $(4, 2)$ , and $(2, 6)$ is transformed into a triangle with vertices at $(1, 1)$ , $(2, 1)$ , and $(1, 3)$ . Which transformation precisely describes this mapping?

Question 6

If a geometric figure undergoes a dilation with scale factor $k = 3$ , the lengths of its sides are tripled. What happens to the interior angles of the image?

Question 7

A translation is defined by the translation vector $\begin{pmatrix} a \\ b \end{pmatrix}$ . Which of the following statements about the distance every point on the object moves is true?

Question 8

Which of the following best explains why the vertical height $h$ cannot be used directly as the height of the triangular faces when calculating a pyramid's surface area?

Question 9

An irregular rock is submerged in a measuring cylinder containing water. The initial water level is $150 \text{ mL}$ , and after the rock is fully submerged, the level rises to $185 \text{ mL}$ . The volume of the rock is ______.

Question 10

If the radius of a sphere is multiplied by a factor of $3$ , by what factor does the total surface area increase?

Practice Geometry of Shapes, Surface Area and Volume with authentic MYP MYP Standard Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

A triangle has vertices at $(1, 2)$ , $(3, 2)$ , and $(1, 5)$ . If the triangle is reflected in the line $y = x$ , what are the coordinates of the vertices of the image triangle?

Question 2

A dilation is centered at the origin with a scale factor of $k = -0.5$ . If the pre-image is a line segment of length $10$ units, what is the length of the image segment and where is it located relative to the center?

Question 3

A small soil sample has a volume of $0.002 \text{ m}^3$ . How many cubic millimeters ( $\text{mm}^3$ ) is this volume?

Question 4

In a right cone, which equation correctly relates the radius $r$ , the vertical height $h$ , and the slant height $s$ ?

Question 5

A triangle with vertices at $(2, 2)$ , $(4, 2)$ , and $(2, 6)$ is transformed into a triangle with vertices at $(1, 1)$ , $(2, 1)$ , and $(1, 3)$ . Which transformation precisely describes this mapping?

Question 6

If a geometric figure undergoes a dilation with scale factor $k = 3$ , the lengths of its sides are tripled. What happens to the interior angles of the image?

Question 7

A translation is defined by the translation vector $\begin{pmatrix} a \\ b \end{pmatrix}$ . Which of the following statements about the distance every point on the object moves is true?

Question 8

Which of the following best explains why the vertical height $h$ cannot be used directly as the height of the triangular faces when calculating a pyramid's surface area?

Question 9

An irregular rock is submerged in a measuring cylinder containing water. The initial water level is $150 \text{ mL}$ , and after the rock is fully submerged, the level rises to $185 \text{ mL}$ . The volume of the rock is ______.

Question 10

If the radius of a sphere is multiplied by a factor of $3$ , by what factor does the total surface area increase?