Will you please attempt this question!?? Exam is tomorrow and I need your help!Two cuboids are mathematically similar. The smaller one has a shortest edge of 5cm,& its surface area is 400cm^2....

Will you please attempt this question!?? Exam is tomorrow and I need your help!

Two cuboids are mathematically similar. The smaller one has a shortest edge of 5cm,& its surface area is 400cm^2. The larger one has a shortest edge of 8cm. Find the surface area of the larger cuboid.

 

Asked on by diarie

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given the smaller cuboid has a surface area 400 cm^3

Let the dimensions be 5*x1*y1

Then the surface area is given by:

SA = 2*5x + 2*5y + 2*xy = 400

==> 10x1 + 10y1 + 2x1y1 = 400 ..............(1)

Now the larger cuboid.

==> SA = 2*8x2 + 2*8y2 + 2*x2*y2

==> SA = 16x2 + 16y2 + 2x2y2..............(2)

But since both cuboids are similar , then we know that:

x1/x2 = 5/8==> x2= 8/5 x1

 y1/y2 = 5/8 ==> y2 = 8/5 y1

Now we will substitute into (2)

==> SA = 16(8/5)x1 + 16(8/5)y1 + 2(8/5)(8/5)x1y1

==> SA = (128/5)x1 + (128/5)y1 + (128/25)x1y1

Now factor 128/5

==> SA = (128/5)*[ x1 + y1 + (1/5)x1y1]

Now multiply and divide by 10.

==> SA = (128/10*5) [ 10x1+ 10y1 + 2x1y1]

But. from (1),  we know that 10x1+10y1 + 2x1x2 = 400

==> SA = 128/50 * 400 = 1024

Then the surface area is 1024 cm^2

 

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