Question

A rectangular prism with the surface area of 336 and width of 4 is similar to a rectangular prism with the width of 6, what is the surface area of the larger prism

Answer 1

Answer:

The larger surface area would be 756 $Unit^2$

Step-by-step explanation:

Given the surface area of rectangular prism is 336 $Unit^2$ when its width is 4 $Unit$.

We need to compute the surface area when its width is 6 $Unit$.

Also, it was given that prisms are similar to each other.

Let us assume the $l$ is length $b$ is width and $h$ is the height of the prism.

So, the surface area would be

$S=2(lb)+2(bh)+2(hl)$

$336=2(4l)+2(4h)+2(hl)$ Equation (1)

Now, the new width is 6 $Unit$. That is 1.5 times the previous width. And those prisms are similar, which means other dimensions will also be 1.5 times the previous one.

We can write

$b'=1.5\times b=1.5\times 4=6\\l'=1.5\times l\\h'=1.5\times h$

So, the new surface area would be

$S'=2(l'b')+2(b'h')+2(h'l')\\S'=2(1.5\times l\times 1.5\times 4)+2(1.5\times4 \times 1.5\times h)+2(1.5\times h\times 1.5\times l)\\S'=2.25\times 2(l4)+2.25\times 2(h)+2.5\times 2(hl)$

$S'=2.25[2(4l)+2(4h)+2(hl)]$

From Equation (1) we can plug $336=2(4l)+2(4h)+2(hl)$

$S'=2.25\times 336=756\ Unit^2$

So, the larger surface area would be 756 $Unit^2$