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The exact diameter of the moon is 3480km. Arjun measures the diameter of the moon to be 3500km.
- [2]
Determine the percentage error in Arjun's estimate.
Using his measurement, Arjun estimates the surface area of the moon to be A=a×10kkm2, where 1≤a<10.
- [2]
Find a and k.
Arjun uses a millimeter ruler to measure the dimensions of a postage stamp.
The height h of the stamp satisfies the inequality 13≤h<14.
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Write a similar inequality for the width, w, of the stamp.
- [4]
Using Arjun's measurements, estimate the minimum number of stamps necessary to cover the moon.
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The rate of heat production of bears is proportional to the cube of its height, measured from foot to shoulder.
A black bear with height 70cm produces heat at a rate of 250W.
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Find an expression for the rate of energy consumption of a bear in terms of its shoulder height, h, in meters.
- [2]
Hence find the rate of heat production of a 120cm brown bear. Give your answer to the nearest 100W.
In the arctic, the rate of heat loss, in Watts, is given by 800h2.
- [2]
Find the minimum shoulder height for a polar bear to survive the arctic cold.
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