Question

The solids are similar give the scale factor, surface area ratio and volume ratio of the figure below

Answer 1

The scale factor of the smaller solid to the larger solid is 1/4 or 0.25. The surface area ratio is 1/16, while the volume ratio is 1/64.

The scale factor describes the ratio between an original object, shape, or drawing and its model.

The scale drawing or model can be scaled up or scaled down, depending on the situation.

We scale up when the model will be greater than the original object and scale down when the model will be less.

Scale factor = Smaller Object/Larger Object = 5/20 = 1/4 = 0.25

Surface area ratio = scale factor squared = 1/4² = 1/16 = 0.0625

Volume ratio = scale factor cubed = 1/4³ = 1/64 = 0.015625

Thus, as a ratio, the scale factor can be stated as a fraction, decimal, or ratio form.

Answer 2

Since the two solids are a similar, the scale factor is:

`(1)/(4)`

The surface area ratio is the square of the scale factor.

Therefore, the surface area ratio is:

`((1)/(4))^2=(1)/(16)`

The volume ratio is the cube of the scale factor.

Therefore, the volume ratio is:

`((1)/(4))^3=(1)/(64)`

Therefore, the the scale factor, surface area ratio and volume ratio are 1/4, 1/16 and 1/64 respectively