Question

Picture contains the question. Use the answer choices at the bottom to fill in the boxes. Reduce and use other ratios given to fit either volume, area or surface area ratios.

Answer 1

Given,

The table of scale factor, ratio of area and ratio of volume is,

Required:

The ratio of area and volume of the similar solids.

The scale factor is 2:3.

The ratio in area is:

`ratio\text{ in area =\lparen}(2)/(3))^2=(4)/(9)=4:9`

The ratio in volume is:

`ratio\text{ in volume=\lparen}(2)/(3))^3=(8)/(27)=8:27`

The ratio of the area is 50:72.

The scale factor of the solid is:

`Scale\text{ factor=}\sqrt{(50)/(72)}=√(50):√(72)`

The ratio in volume is:

`Scale\text{ factor=\lparen}\sqrt{(50)/(72)})^3=\sqrt[3]{50}:\sqrt[3]{72}`

The ratio in the volume is 27:64.

The scale factor of the solid is:

`Scale\text{ factor=}\sqrt[3]{(27)/(64)}=3:4`

The ratio in the area is,

`Ratio\text{ of area =}(3^2)/(4^2)=(9)/(16)=9:16`

Hence, the ratio of area and volume of the solids is obtained.