Answer:
The ratio between their surface areas = 49/9
Step-by-step explanation:
* Lets revise the similarity of to prism
- If two prisms are similar, then there is a ratio between their
corresponding dimensions
- There is a ratio between their volumes and surface area
- The the ratio between their corresponding dimensions is a/b,
then the ratio between their volumes is (a/b)³ and the ratio between
their surface area is (a/b)²
* Lets solve the problem
∵ The two rectangular prisms are similar
∵ The ratio between their corresponding sides is 7/3
∴ The ratio between their surface areas = (7/3)² = 49/9
* Lets check our answer
∵ The surface area of the rectangular prism is :
S.A = Perimeter of base × its height + 2 × area of its base
- Find the surface area of the large prism
∵ The base has dimensions 14 units and 21 units
∵ Its height = 7 units
∵ The base is a rectangle
∵ Perimeter the rectangle = 2L + 2W
∵ Area the rectangle = L × W
∴ S.A = (2×14 + 2×21) × 7 + 2(14 × 21) = 1078 unit²
- Find the surface area of the small prism
∵ The base has dimensions 6 units and 9 units
∵ Its height = 3 units
∴ S.A = (2×6 + 2×9) × 3 + 2(6 × 9) = 198 unit²
- Lets find the ratio between them
∴ The ratio between surface areas of them = 1078/198 = 49/9
- It is the same with the answer above so we are right
