IB Mathematics Applications & Interpretation Topic SL 3.1—3d Space, Volume, Angles, Midpoints Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 3.1—3d Space, Volume, Angles, Midpoints Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 3.1—3d Space, Volume, Angles, Midpoints with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.1—3d Space, Volume, Angles, Midpoints and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

A company stores cold brew concentrate in conical canisters that have a radius of 7 cm and a vertical height of 24 cm. Designers are evaluating whether these conical canisters can be replaced with cylindrical ones that have the same base radius and the same total surface area.

Calculate the slant height of the conical canister.

[2]

Determine the volume of the conical canister.

[2]

Verify that the total surface area of the conical canister is $704 cm^{2}$ , rounded to three significant figures.

[3]

Calculate the height, $h$ , of the cylindrical canister described.

[4]

The company wants to maximize the liquid volume held in each container. Determine whether the company should transition to cylindrical canisters. Provide a justification for your answer.

[4]

Question 2

SLPaper 2

A rectangular atrium has opposite corners $O (0, 0, 0)$ and $G (6, 8, 24)$ metres. A cable runs along the diagonal $O G$ , and a spherical light is centred at the midpoint $M$ of $O G$ .

Calculate the length of $O G$ .

[2]

Determine the volume of the atrium.

[2]

Verify that the angle between $O G$ and the floor is $67. 4^{\circ}$ , correct to one decimal place.

[3]

Calculate the coordinates of $M$ and the distance from $M$ to the floor.

[4]

A spherical light of radius $3.5$ m is centred at $M$ . Determine whether it fits entirely inside the atrium. Provide a justification.

[4]

Question 3

SLPaper 2

A factory packages coconut water in cone-shaped containers with a base radius of 5.2 cm and a height of 13 cm.

The factory designers are currently investigating whether a cone-shaped container can be replaced with a cylinder-shaped container with the same radius and the same total surface area.

Find the slant height of the cone-shaped container.

[2]

Show that the total surface area of the cone-shaped container is 314 cm², correct to three significant figures.

[3]

Find the height,

h

, of the cylinder-shaped container with the same radius and total surface area as the cone-shaped container.

[4]

The factory director wants to increase the volume of coconut water sold per container.

State whether they should replace the cone-shaped containers with cylinder-shaped containers. Justify your conclusion.

[4]

Question 4

SLPaper 1

A glass ornament is a tetrahedron with vertices $A (0, 0, 0)$ , $B (8, 0, 0)$ , $C (0, 6, 0)$ and $D (0, 0, 9)$ , where coordinates are in cm. $M$ is the midpoint of $B C$ .

Calculate the volume of the tetrahedron.

[3]

Determine the angle between $D M$ and plane $A B C$ .

[3]

Question 5

SLPaper 1

A carved wooden ornament is a square-based pyramid with base edge $10$ cm and face slant height $13$ cm.

Calculate the volume of the pyramid.

[3]

An alternative ornament is a cone of radius $5$ cm with the same volume. Determine its perpendicular height.

[3]

IB Mathematics Applications & Interpretation SL 3.1—3d Space, Volume, Angles, Midpoints Questionbank

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IB Mathematics Applications & Interpretation SL 3.1—3d Space, Volume, Angles, Midpoints Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.1—3d Space, Volume, Angles, Midpoints Questionbank

Unlock all 45 questions with a free account