9. The volume of air in a hemispherical dome is 25 ⋅ 3 metres3 Calculate the radius of the dome to the nearest metre.


Taking it FURTHER


.


10. A new perfume in a 36 mm (internal) diameter spherical bottle is now available in the shops.


(i)


If the bottle is full to the top of the sphere, calculate the total volume in mm3


of perfume it contains.


(ii) How many millilitres (ml) of perfume does the bottle contain?


(iii) The price of the perfume is €80. How much does the perfume cost per ml? Give your answer in euros and cents.


36 mm


Revision questions


3A Core skills 1. Calculate the area of the shapes shown. Give your answers as whole numbers. 3 cm


(i) (ii) 1 cm 5 cm 5 cm


2. Jenny is planning a new garden that is in the shape of a parallelogram. It has two ponds and a fl ower bed. The rest of the space will be fi lled with grass.


The plan of the garden has been drawn to scale on a 1 cm grid. Scale: 1 cm = 4 m


Find the area of the following: (i) both ponds (ii) the fl ower bed (iii) the total area of the garden (iv) the area of the garden that will be covered with grass.


3. The diagram shows the fl oor plan of a hotel lobby. (i) Calculate the total area of the fl oor.


(ii) The hotel manager wishes to purchase some carpet to cover the fl oor. The carpet costs €27 ⋅ 99 per m2 How much will it cost to fully carpet the fl oor?


.


(iii) The manager also purchases a brass border to cover the edges of the carpet along the wall. The border costs €8·99 per metre and is only sold in 5 metre lengths, calculate:


(b) the total cost of the border. Section A Applying our skills 75 Pond Pond 3 cm 3 cm 3 cm 12 cm


Flower bed


Grass (iii) 9 cm (iv)


6 cm


A 6 cm B 8 cm C 7 cm E


(a) the total length of border needed (Hint: you may need to use Pythagoras’s theorem to fi nd the missing length, |DG|)


10 cm F G


D


3 Volume, surface area and nets of 3D solids


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