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Zorluk: OrtaRectangular Volume and Container Capacity

Service members are constructing a rectangular wooden planter box for a community project. The interior dimensions of the planter are 1616 feet in length and 44 feet in width. A delivery of 128128 cubic feet of potting soil fills the planter perfectly to a level exactly 66 inches below its top edge. What is the total interior height of the planter, in feet?

  1. A
    2.02.0
  2. 2.52.5Cevap
  3. C
    2.62.6
  4. D
    8.08.0

Cevap

The total interior height of the planter is 2.52.5 feet.
To find the total height, first determine the height of the soil. Since Volume = Length × Width × Height, the soil height is 128÷(16×4)=2128 \div (16 \times 4) = 2 feet. The problem states there is a 66-inch gap at the top. Converting 66 inches to feet gives 0.50.5 feet. Adding the soil height and the gap gives a total interior height of 2+0.5=2.52 + 0.5 = 2.5 feet.

Adım Adım Çözüm

1
Calculate the area of the planter's rectangular base.
16×4=6416 \times 4 = 64 square feet.
The base area is required to determine how deep the potting soil will sit.
2
Calculate the depth of the potting soil.
128÷64=2128 \div 64 = 2 feet.
Dividing the total volume of soil by the base area yields the height (or depth) of the soil layer.
3
Convert the remaining empty height from inches to feet.
6 inches=0.5 feet6 \text{ inches} = 0.5 \text{ feet}.
All measurements must be in the same unit (feet) before they can be added together.
4
Add the soil depth to the empty space depth.
2+0.5=2.52 + 0.5 = 2.5 feet.
The total interior height is the sum of the filled space and the empty space.

Anahtar Kavram

Solving for a missing dimension in a rectangular volume and ensuring measurement units are consistent.
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Konular

Rectangular Volume and Container Capacity

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