4. Brona has a tablet. The dimensions are provided in the diagram to the right.


(i) Calculate the total area of the front of tablet.


(ii) Calculate the area of the screen.


12 cm


(iii) Brona states that the border of her tablet is only 1


__ 10 of the total area of the front.


5. The volume of a cube is 64 cm3


Is she correct? Justify your answer. .


(i) What is the length of one edge of the cube? (ii) What is the area of one face of the cube?


6. Sketch a net of this rectangular solid.


(i) Calculate its surface area.


1 cm 40 mm (ii) Calculate its volume in cm3 .


7. Find the volume of the following cylinders. Give your answer to two decimal places.


Cylinder Radius Height A


B C D E


5 cm 9 cm 11 cm 0·30 m 2·7 m 200 cm


_ 1 000 km 3


1


_ 1 000 km


0·2 mm 3 cm


8. How many square tiles measuring 20 cm by 20 cm are needed to cover the sides and base of a pool that is 10 m long, 6 m wide and 3 m deep?


9. The inside dimensions of a wooden sand pit for a local playground are 2 m by 3 m by 25 cm. The sandbox is a rectangular solid.


(i) Calculate the internal surface area of the sand pit.


(ii) Calculate the maximum volume of sand it will hold. Assume that the maximum volume of sand is level with the top of sand pit.


5 cm


9 cm 13 cm 15 cm


1. A window washing company is hired to wash the windows in an apartment block. The building is 60 m by 40 m by 200 m. Windows cover one-third of the building.


What is the total surface area of the windows to be washed? Give your answer to the nearest whole m2


.


2. Out of the rectangular solids A, B and C shown below, which rectangular solid has …?


(i) the greatest surface area (ii) the least surface area Justify your answer in each case.


A 4 cm 2 cm 6 cm B 3 cm 1 cm 8 cm C 4 cm 5 cm 3 cm


3. A rectangular solid has a square base with an area of 16 m2 shape is 48 m2


. What are the dimensions of the shape?


4. The diagram shows a wooden doorstop. The doorstop needs to be painted. The bottom rectangular face is covered with rubber and will not be painted.


16.7 cm 15.9 cm


Find the total surface area to be painted. Give your answer correct to one decimal place.


5. A rectangular swimming pool is to be fi lled with water. The pool has a uniform (constant) depth of 2 m and is surrounded by a wooden decking. The pool is 10 m wide and 25 m long.


(a) How much water, in metres cubed, is needed for each of the following situations?


(i) The pool is fi lled to the level of the decking.


(ii) The pool is fi lled to 15 cm below the level of the decking. Give your answer to three decimal places.


(b) How many litres of water are needed for the pool to be 50% full?


Section B Moving forward 281 . The total surface area of the


17B Taking it FURTHER


5.0 cm 8.9 cm


17 Area, volume and surface area


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