Chapter 12.8, Problem 22HP

To determine

To find: The ratio of surface area and volume of model of car.

Answer to Problem 22HP

Ratio of surface area = 1:4

Ratio of volumes = 1:8

Explanation of Solution

Given: A model of car is given.

Let the scale factor of model of car is 1:24.

The dimension of model of car is 3 in high, 2.5 in wide and 6.5 in long.

Now find the ratio of surface and volume of the model of car.

First find the surface area of model of car $=2\left(3\times 2.5+2.5\times 6.5+6.5\times 3\right)=86.5{\text{ in}}^2$

Now find the surface area of actual car $=2\times 2\times 2\left(3\times 2.5+2.5\times 6.5+6.5\times 3\right)=346{\text{ in}}^2$

Now find the ration model to actual surface area is 1:4

Now find the volume of car model $=3\times 2.5\times 6.5=48.75{\text{ in}}^3$

Volume of actual shape of car $=3\times 2.5\times 6.5\times 8=390{\text{ in}}^3$

The ratio of volume of model to actual volume of car is 1:8