Answer :
a. The amount of paint required for the single plane in Case A be equal to the total amount of paint required for all four planes in Case B
b. The weight of the single plane in Case A be greater than the total weight of all four planes in Case B
What is volume?
The capacity of a geometry is called as volume.
A woodworker has made four small airplanes and one large airplane. All airplanes are exactly the same shape, and all are made from the same kind of wood. The larger plane is twice as large in every dimension as one of the smaller airplanes. The planes are to be painted and then shipped as gifts.
a. The amount of paint required to paint the planes is directly proportional to the surface area.
As the shapes of the large and the small plane are similar, k =2
The ratio of surface areas will be
Slarge /Ssmal = k² = (2)² =4
Slarge = 4 x Ssmall
If the small plane requires where the amount of paint, P
The large plane requires 4P.
4 small planes require 4P.
4 small planes require the same amount of paint as 1 large plane.
b. The shipping cost of the planes is proportional to the weight, which is related directly to the volume.
As the shapes of the large and the small plane are similar, k =2
The ratio of volumes will be
Vlarge /Vsmall = k³ = (2)³ =8
Vlarge = 8 x Vsmall
If the small plane weighs where W = density x Vsmall
The large plane weighs 8W
4 small planes weigh 4W
Thus, 4 small planes weight less than 1 large plane.
Learn more about volume.
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