Area and volume > EnlargementsExercises
Working on a large bronze sculpture, an artist first makes a scale model at . The scale model has a surface of cm2 and a volume of cm3.
Calculate the surface and volume of the bronze sculpture.
A particular type of paint comes in tins of liter or liter. These tins have the same shape.
How many times taller is the liter tin than the liter tin?
If both tins are made from a metal sheet of the same thickness, how much more metal will be used for the liter tin? And how much more would be used if the metal sheet would need to be proportionally thicker?
In his book "Gulliver's travels" , Jonathan Swift writes about the inhabitants of Lilliput. These imaginary people look like real humans shrunk by a factor . Assume such a Lilliputian was a perfect shrunk copy of yourself.
How tall would this Lilliputian be?
How much would this Lilliputian weigh?
How much less skin surface would this Lilliputian have compared to you?
The food requirement of mammals is approximately directly proportional to their skin surface, since food is primarily required to maintain body temperature and the loss of heat is dependent on surface area. Estimate how many grams of food you consume each day and then calculate how much the Liliputian would have to eat.
What percentage of your body weight do you eat every day? And the Lilliputian?
Why is the energy requirement of mammals proportional to the square of their height?
Explain why the amount of food per kg body weight is proportional to , where is body length.
Inside a cube-shaped pot with edges of cm a solid cone stands on the base area . This cone touches all edges of the base of the cube and its top is located straight above the middle of the base area. The cube is open at the top and the cone sticks out such that only of it is inside the cube.
How tall is this cone?