1. Jessica has one cube with a side length of \(4\) and another cube with a side length of \(5.\) She then glues the two cubes together, to form one single solid. What is the smallest possible surface area of the single solid?
2. In the rectangular prism below, the area of face \(TUVW\) is \(6\), the area of face \(TUQP\) is \(15\), and the area of face \(TPSW\) is \(40.\) Find the volume of the rectangular prism.
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Thank you!
+23245 1) A cube with side length = 4 has an area of 16 for each of its sides; 6 x 16 = 96 for its total area.
A cube with side length = 5, has an area of 25 for each of its sides; 6 x 25 = 150 for its total area.
The total area for both is 96 + 150 = 246
If you glue one of the sides of the smaller cube to one of the sides of the larger cube, you will remove 16
from each of the two cubes: 246 - 16 - 16 = 214
2) length = L
width = W
height = H
L · W = 6 ---> W = 6 / L
W · H = 15 ---> W = 15 / H
L · H = 40
Since W = 6 / L and W = 15 / H ---> 6 / L. = 15 / H ---> 6H = 15L ---> H = 15L / 6
Since L · H = 40 ---> L · ( 15L / 6 ) = 40 ---> 15L2 = 240 ---> L2 = 16 ---> L = 4
Since L = 4 ---> L · W = 6 ---> 4 · W = 6 ---> W = 1.5
Since L · H = 40 ---> 4 · H = 40 ---> H = 10
