4. The area of the base of each prism (i)–(iv) is given. Calculate the heights. Give your answers to one decimal place, where necessary. (i)
(ii) (iii) (iv) 29 cm2 Volume = 392 cm3 40 cm2 h h Volume = 180 cm3 Volume = 677 ⋅ 74 m3 72.1 m2 h
4 mm2 h Volume = 46 ⋅ 88 mm3
5. A solid cylinder has a diameter of 15 cm and a height of 26 cm. (i) Find the volume of the cylinder. Give your answer to three signifi cant fi gures. (ii) Find the total surface area of the cylinder. Give your answer to one decimal place.
6. Air is leaking from a spherical advertising balloon at the rate of 9 m3 per minute.
If the radius of the balloon is 1 ⋅ 5 metres, calculate how long it will take for the balloon to empty fully. Round your answer to the nearest minute. (Let π = 3 ⋅ 14)
7. The diagram shows a large tin of pet food in the shape of a cylinder. The tin has a radius of 6 ⋅ 5 cm and a height of 11 ⋅ 5 cm. A pet food company wants to make a new size of tin. The new tin will have a radius of 5 ⋅ 8 cm. It will have the same volume as the fi rst tin.
(i) Calculate the height of the new tin. Give your answer correct to one decimal place.
(ii) The company wants to create a label to completely surround the curved surface area of the new tin. Calculate the minimum area of the label required.
8. The volume of Earth is 1·08 × 1012 The volume of Jupiter is 1·43 × 1015
km3 . km3 .
Assuming both Earth and Jupiter are spheres, calculate: (i) The radius of Earth (ii) The radius of Jupiter
(iii) By how many percent is the radius of Jupiter larger than the radius of Earth? Give all answers to the nearest whole number.
9. Daisy wants to fi ll 12 hanging baskets with compost. Each hanging basket is a hemisphere with an internal diameter of 40 cm. She has four bags of compost. There are 50 litres of compost in each bag.
(i) Calculate the volume of one hanging basket.
(ii) Does Daisy have enough compost to fi ll the 12 hanging baskets? Justify your answer.
1 000 cm3
10. You have a number of rectangular tiles with a length of x cm and height of ( x + 7) cm. Some of these tiles are used to form the shape shown, which is six tiles long and four tiles high.
(i) Write expressions, in terms of x , for (a) the length and (b) the height of this shape.
The length and the height of this shape are equal. (ii) Write down an equation in terms of x to represent this. (iii) Solve this equation to fi nd the value for x . (iv) Hence, or otherwise, calculate the area of this shape.
76 Linking Thinking 2 height
= 1 litre x
x + 7 length 6.5 cm 11.5 cm
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