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Yr12FM SAC 2 REVISION Geometry Name: ___________________________ (SOLUTIONS) Section A Multiple Choice 1 Examine the triangle in the following figure. 4 The value of x is: A 33 B 59 C 68 D 90 E 57 2 An appropriate name for the object is: A rectangular prism B rectangular pyramid C triangular prism D triangular pyramid E trapezium prism Examine the following figure. 5 The volume of a sphere with a diameter of 15 cm is closest to: A 560 π cm3 B 900 π cm3 C 4500 π cm3 D 36 000 π cm3 E 45 000 π cm3 6 The circumference of the base of the larger cone is closest to: The area of the shape is: A (130 000 + 10 000π) mm² B (160 000 + 10 000π) mm² C (160 000 + 5000π) mm² D (130 000 + 5000π) mm² E 30 100 mm² 3 The total surface area of a closed cylinder of radius 40 cm and height 20 cm is given by: A 2 π 20 40 B 2 π 40 40 C 2 π 40 100 D 2 π 40 60 E 2 π 20 60 Consider the net of the following figure. A B C D E 113 mm 151 mm 190 mm 302 mm 459 mm 1 7 If the height of a flag with diagonal = 68 cm is 90 cm, then a similar flag with diagonal = 34 cm has a height closest to: A 67 cm B 45 cm C 30 cm D 26 cm E 34 cm 8 The diagram shows the path of a light beam hitting a mirror. 9 Find the length of the side a (to the nearest m). A 14 m B 15 m C 16 m D 17 m E 18 m The expression for x is: A B C D E 6 6 x 4 x 4 6 x 6 x 6 x6 4 x 12 6 x 6 x 6 2 x 4 x A monster slice of pizza is made in the shape below. 10 A large cone is filled to half its height with water as shown. The ratio of the volume of water to air is: A 1:7 B 1:8 C 8:1 D 1:9 E 1:2 2 11 Given that you have a two-litre and a one-litre carton of milk in the same shape (similar dimensions), the length scale factor of the two-litre to the onelitre carton is: A 2:1 B 1:2 C 2: 2 3 D 2:1 E 8:1 3 Yr12FM SAC 2 REVISION Geometry Name: ___________________________ (SOLUTIONS) Section B Short/Extended answer 1 For each of the figures, find the value of the pronumeral. (a) 5 (b) 2 Find the interior and exterior angles for each of the following regular polygons. (a) Octagon (b) Heptagon (c) Nonagon 3 4 3 Find the perimeter and area of the following figures. (a) 6 (b) 5 4 Examine the solid prism below. 3 (a) Sketch an appropriate net for the given prism. (b) Transfer the units appropriately to the net. (c) Calculate the total surface area of the object. 5 Examine the diagram below. 4 For the object shown: (a) What is the volume contained by the solid and framed sections (to 1 decimal place)? (b) What is the volume of the solid part only? 6 6 The dimensions of a rectangular prism tub are 30 cm by 20 cm by 15 cm. The tub is filled completely with water, and the water is transferred into a cylindrical tank that is 10 cm in radius and 40 cm tall. How high is the water level in the cylinder? 5 7 Two ladders are placed against the wall at the same angle. The ladders are 2 metres and 3 metres long. If the taller ladder reaches 2.1 metres up the wall, how far does the second ladder reach (to 1 decimal place)? 3 8 Note the following measurements from the buoy to the shore as shown in the diagram below. 3 How far is it to the buoy (to the nearest metre)? (This is the distance x on the diagram.) 7 9 A rectangular block of clay has dimensions 30 cm by 20 cm by 10 cm. 3 (a) What is the volume of the block of clay? (b) Express in litres your answer from (a). (c) What is the total surface area of the clay? 10 The clay from question 9 is remolded into a cylinder with height 30 cm. 6 (a) Find the diameter of the cylindrical block of clay (to 2 decimal places). (b) Find the new total surface area of the clay when molded as a cylinder (to the nearest cm²). (c) What fraction of the volume needs to be removed to turn the cylindrical block into a cone with the same diameter and height? 11 A windscreen wiper covers the shaded area below. 3 Find the area of the rectangular windscreen that is not covered by the windscreen wiper (to the nearest cm²). 8