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Zorluk: OrtaVolume and Surface Area of 3D Figures

A shipping company uses rectangular boxes that measure 44 feet in length, 33 feet in width, and 22 feet in height. The company needs to completely cover the outside of one box with a protective weather-resistant wrapping. How many square feet of wrapping are required?

  1. A
    14
  2. B
    24
  3. C
    26
  4. 52Cevap

Cevap

52
The question asks for the amount of wrapping needed to completely cover the outside of the box, requiring the total surface area of a rectangular prism. Using the formula SA=2(lw+lh+wh)SA = 2(lw + lh + wh) and substituting the dimensions l=4l = 4, w=3w = 3, and h=2h = 2 yields SA=2((4)(3)+(4)(2)+(3)(2))=2(12+8+6)=2(26)=52SA = 2((4)(3) + (4)(2) + (3)(2)) = 2(12 + 8 + 6) = 2(26) = 52 square feet.

Adım Adım Çözüm

1
Identify the required measurement
Calculate the total surface area of the rectangular prism.
The problem asks for the amount of wrapping needed to 'completely cover the outside', which corresponds to surface area rather than volume.
2
Recall the surface area formula for a rectangular prism
SA=2(lw+lh+wh)SA = 2(lw + lh + wh)
A rectangular box has six faces, composed of three identical pairs of rectangles (top/bottom, front/back, left/right).
3
Substitute the given dimensions and solve
SA=2((4)(3)+(4)(2)+(3)(2))=2(12+8+6)=2(26)=52SA = 2((4)(3) + (4)(2) + (3)(2)) = 2(12 + 8 + 6) = 2(26) = 52 square feet.
Applying the measurements l=4l=4, w=3w=3, and h=2h=2 evaluates the total combined area of all six faces.

Anahtar Kavram

Calculating the total surface area of a rectangular prism.
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Konular

Volume and Surface Area of 3D Figures

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