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

The larger surface area would be 756

Step-by-step explanation:

Given the surface area of rectangular prism is 336 when its width is 4 .

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

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

Let us assume the is length is width and is the height of the prism.

So, the surface area would be

Equation (1)

Now, the new width is 6 . 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

So, the new surface area would be

From Equation (1) we can plug

So, the larger surface area would be 756

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2