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A company makes fish tanks in the shape of right rectangular prisms. The company has an order for a fish tank that must be exactly 4 feet long and hold at least 35 cubic feet of water. The company wants to save money on materials and will make the tank with the smallest surface area possible. The dimensions of the tank must be in whole foot increments and a top is included in the construction What dimensions for the width and height of the fish tank will satisfy the requirements

Sagot :

The dimensions for the width and height of the fish tank will be 4 feet and 2 feet .

What is dimension?

Dimension is the measurable extent of a particular kind, such as length, breadth, depth, or height.

According to the given problem,

let , b = is the width of the fish tank

h = is the height of the fish tank given that , hold at least 35 cubic feet of water .

so ,

4×b×h ≥ 35

⇒ h ≥ 35/4b

now , surface area of the fish tank

⇒ 4b + 2× 4h + 2× bh

now substitute the value of h

here

⇒ ≥ 4b +70/b + 35/2

⇒ ≥ 40(70)^1/2 + 35/2 (if and only if b= (70)^1/2 / 2 , the equal sign holds )

therefore ,

= (70)^1/2 / 2 b ≈ 4.18 so b is 4 . when b = 4 ,

h = 35 / 4 × 4 = 2.1875 round off h = 2

so , the minimum surface area of fish tank is

⇒ 4×4+ 2× 4×2 + 2× 4×2⇒ 48

hence , the height and the width of the fish tank is 2 and 4 .

learn more about dimension here :brainly.com/question/27022535

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