The area of the base of a cube is given by the function A(V) = v2/3, where V = 3,375 in3 is the volume of the cube. In a preschool room, 18 children's cubicles like that shown are placed on the floor around the room. Estimate how much floor space is lost to the cubicles. Mary S Storage сараcity V in3 Give your answer in square inches. in? Give your answer in square feet. (Round your answer to the nearest whole number.)
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![### Calculating Floor Space Occupied by Cubicles in a Preschool Room
#### Problem Statement
The area of the base of a cube is given by the function \( A(V) = V^{2/3} \), where \( V = 3,375 \, \text{in}^3 \) is the volume of the cube. In a preschool room, 18 children's cubicles like the one shown are placed on the floor around the room. Estimate how much floor space is lost to the cubicles.
#### Image Description
The image visually represents a cubicle with a storage capacity of \( V \, \text{in}^3 \). This cubicle is labeled "Mary S." and contains various items.
#### Solving the Problem
1. **Calculate the Area of the Base of One Cubicle:**
\[
A(3375) = 3375^{2/3}
\]
2. **Total Floor Space for 18 Cubicles:**
\[
\text{Total Floor Space} = 18 \times A(3375)
\]
3. **Convert the Answer from Square Inches to Square Feet:**
\[
1 \, \text{ft}^2 = 144 \, \text{in}^2
\]
#### Questions:
1. **Give your answer in square inches.**
\[
\boxed{\text{in}^2}
\]
2. **Give your answer in square feet. (Round your answer to the nearest whole number.)**
\[
\boxed{\text{ft}^2}
\]
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