Answer:
a) If the volume of the prism on the left is 1029 m³, then the volume of the prism on the right is 1536 m³.
b) If the height of the prism to the left is 14 m, the height of the prism to the right will be 16 m.
c) If the surface area of the prism to the left is 392 m², the surface area of the prism to the right will be 512 m².
Explanation:
a) To solve, set up a proportion. Volume is three-dimensional, so we need to cube.
(7/8)³=1029/x
Now we can solve using cross products to get 1536.
If the volume of the prism on the left is 1029 m³, then the volume of the prism on the right is 1536 m³.
b) To solve the second one, we also set up a proportion. Height is one-dimensional, so we will not need exponents here.
7/8=14/x
Solve using cross products to get 16.
If the height of the prism to the left is 14 m, the height of the prism to the right will be 16 m.
c) Now we are solving for area, which is two-dimensional. Therefore, we will need to square.
7/8²=392/x
Solve using cross products to get 512.
If the surface area of the prism to the left is 392 m², the surface area of the prism to the right will be 512 m².
Hope this helps and good luck on your homework! For additional resources, check out The Maths Prof: Similarity parts 1-3.