A small animal is modelled as a ball of radius 1.5 cm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A small animal is modelled as a ball of radius cm. A large animal is modelled as a ball of radius cm.
- What is the surface area for each cm³ of the small animal?
- What is it for the large animal?
- How many times more surface for each unit of volume does the small animal have?
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 and cm.
Plan. The ratio of surface to volume is .
Step 1. (a) per cm.
Step 2. (b) per cm.
Step 3. (c) times. This is also , the ratio of the radii.
Answer: per cm; per cm; times.
Check. The ratio of the two ratios is the ratio of the radii, upside down.
What if? The small animal loses heat times faster for each unit of body, so it must make heat times faster to stay warm.
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