Three animals are modelled as balls of radius 2 cm, 4 cm and 8 cm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Three animals are modelled as balls of radius cm, cm and cm.
- What is the surface area for each cm³ of volume of the smallest ball?
- What is it for the ball of radius cm?
- What is it for the ball of radius cm?
Need a reminder? The key ideaShow
A ball of radius has the surface area and the volume . So its surface for each unit of volume is . Allen's rule: shorter ears and limbs in cold climates. At high altitude, the body makes more red cells, haemoglobin binds oxygen less, and breathing is faster.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. cm. The ratio is .
Plan. Divide by each radius.
Step 1. (a) per cm.
Step 2. (b) per cm.
Step 3. (c) per cm.
Answer: ; ; per cm.
Check. Each doubling of the radius halves the ratio.
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