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# difficult questions :(

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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.

Image for #2: Thank you!

Apr 15, 2020

#1
+1

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

Apr 15, 2020
#2
+1

I feel so stupid it all fell into place. Argh. Thank you so much.

Apr 15, 2020