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Len [333]
3 years ago
6

What is the lateral surface area of a rectangular prism in square inches.

Mathematics
1 answer:
natulia [17]3 years ago
4 0

Answer:

When a prism has its bases facing up and down, the lateral area is the area of the vertical faces.

(For a rectangular prism, any pair of opposite faces can be bases.)

The lateral area of a right prism can be calculated by multiplying the perimeter of the base by the height of the prism.

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If an open box has a square base and a volume of 115 in.3 and is constructed from a tin sheet, find the dimensions of the box, a
Karolina [17]
Let h = height of the box,
x = side length of the base.

Volume of the box is  V=x^{2} h = 115. 
So h = \frac{115}{ x^{2} }

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
S = 2( x^{2}  + hx + hx)  \\ = 2 x^{2}  + 4hx  \\  = 2 x^{2}  + 4( \frac{115}{ x^{2} } )x
= 2 x^{2} + \frac{460}{x}
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

S' = 4x- \frac{460}{ x^{2} }  = 0
4x = \frac{460}{ x^{2} }  \\  4x^{3} = 460  \\ x^{3} = 115  \\ x =  \sqrt[3]{115} = 4.86
Then h=  \frac{115}{4.86^{2}} = 4.87
So the box is 4.86 in. wide and 4.87 in. high. 

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3 years ago
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What do we do to both sides of this equation to solve?
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Answer:

Subtract 3 from both sides.

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x + 3 = 5

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I know I`m late sorry, still wanted to answer

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3 0
2 years ago
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