Service members are constructing a rectangular wooden planter box for a community project.… — Armed Services Vocational Aptitude Battery (ASVAB)

Service members are constructing a rectangular wooden planter box for a community project. The interior dimensions of the planter are $16$ feet in length and $4$ feet in width. A delivery of $128$ cubic feet of potting soil fills the planter perfectly to a level exactly $6$ inches below its top edge. What is the total interior height of the planter, in feet?

A
$2.0$
$2.5$ Answer
C
$2.6$
D
$8.0$

Answer

The total interior height of the planter is

2.5

feet.

To find the total height, first determine the height of the soil. Since Volume = Length × Width × Height, the soil height is

128 \div (16 \times 4) = 2

feet. The problem states there is a

6

-inch gap at the top. Converting

6

inches to feet gives

0.5

feet. Adding the soil height and the gap gives a total interior height of

2 + 0.5 = 2.5

feet.

Step-by-Step Solution

Calculate the area of the planter's rectangular base.

16 \times 4 = 64

square feet.

The base area is required to determine how deep the potting soil will sit.

Calculate the depth of the potting soil.

128 \div 64 = 2

feet.

Dividing the total volume of soil by the base area yields the height (or depth) of the soil layer.

Convert the remaining empty height from inches to feet.

6 \text{ inches} = 0.5 \text{ feet}

All measurements must be in the same unit (feet) before they can be added together.

Add the soil depth to the empty space depth.

2 + 0.5 = 2.5

feet.

The total interior height is the sum of the filled space and the empty space.

Key Concept

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

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