PART A: MULTIPLE CHOICE (one (1) mark for each question)

For questions 1 to 5, select the best answer.

1. What is the area of the figure?  (C1)

A 57.25 m² B 39 m² C 63.5 m² D 66 m²

• What is the volume of the square-based prism?  (C1)

A 5.75 cm³          B 510 mm³                   C  0.575 cm³                          D  580 mm³

• What is the surface area of the prism in question 2?  (C1)

A 535 cm²            B 580 mm²                   C  485 mm²                        D  510 mm²

C1  ______

3

MAP4C:  Grade 12, Foundations for College Mathematics

• What is the volume of the cylinder?  (C1)

• A box in the shape of a square-based prism is to have a volume of 900 cm³. What are the approximate dimensions of the prism that give the minimum surface area? (C2)

A 10 cm, 10 cm, 9 cm B 9 cm, 9 cm, 11.1 cm

C 9.65 cm, 9.65 cm, 9.65 cm D 9.5 cm, 9.5 cm, 10 cm

PART B: FULL SOLUTION: For the following questions, show your all work in the space provided

• Determine the volume of metal used to make this pipe. The pipe has a thickness of 5 mm. Discuss any assumptions you made. (4 marks) – (C1)

MAP4C:  Grade 12, Foundations for College Mathematics

• This patio is to be painted with water sealant. Determine the area to be painted, to the nearest metre. (4 marks) – (C1)

• Two book ends are n the shape of trapezoidal prisms.  Each is made of marble.

1. What is the volume of marble in one set of two bookends? (3 marks) – (C1)

• An artist has a 0.25-m³ block of marble. How many sets of bookends can be made? List any assumptions you made. (2 marks) – (C1)

C1  ______

9

MAP4C:  Grade 12, Foundations for College Mathematics

• A storage container in the shape of a square-based prism has a base length of 2.6 yd and a height of 5.5 yd.

1. Determine the surface area of the container, to one decimal place. (3 marks) – (C1)

• Determine the volume of the container to one decimal place. (3 marks) – (C1)

• For this volume, determine the dimensions of the container with minimum surface area. (3 marks) – (C2)

1. Tamara has 30 m of fencing which she can use to surround a rectangular garden. What is the maximum area of the garden, assuming Tamara uses fencing for all four sides? (3 marks) – (C2)

MAP4C:  Grade 12, Foundations for College Mathematics

1. A cylindrical shampoo container is to have volume 759 cm³.

a) Determine the dimensions of the container with minimum surface area.(3 marks) – (C2)

• Sketch the container and label its dimensions. (1 mark) – (C2)

• Determine the minimum surface area. (3 marks) – (C2)

C2  ______

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