Use 3.14 for π. Round each value to the nearest whole unit....

Use 3.14 for $\pi .$ Round each value to the nearest whole unit. Richard needs 3 in. of topsoil for his vegetable garden that is in the shape of a rectangle, $15 \mathrm{ft}$ by $20 \mathrm{ft}$. a. Find the amount of topsoil needed in cubic feet. b. If topsoil can be purchased in bags containing $2 \mathrm{ft}^{3},$ how many bags must Richard purchase?

Use 3.14 for $\pi .$ Round each value to the nearest whole unit.
Richard needs 3 in. of topsoil for his vegetable garden that is in the shape of a rectangle, $15 \mathrm{ft}$ by $20 \mathrm{ft}$.
a. Find the amount of topsoil needed in cubic feet.
b. If topsoil can be purchased in bags containing $2 \mathrm{ft}^{3},$ how many bags must Richard purchase?

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Key Concepts

Area of a Rectangle

This concept involves calculating the area of a rectangular surface by multiplying its length by its width. It is fundamental in determining the base over which other calculations, such as volume, are built, ensuring that dimensions are correctly applied and that the proper units are used.

Volume Calculation for a Rectangular Prism

Volume calculation for a rectangular prism is done by multiplying the floor area (taken from length and width) by the height or depth of the material. This method applies to situations where a uniform layer (such as topsoil) is spread across a flat, rectangular area.

Unit Conversion

Unit conversion is critical when dealing with measurements given in different units. In this context, it involves converting the depth from inches to feet to maintain consistency with the dimensions of the rectangle. Standard conversion factors ensure that calculations remain accurate across units.

Rounding and the Ceiling Function

Rounding and the ceiling function are important when an exact value is impractical to purchase or use. After calculating the needed volume, rounding to the nearest whole unit or using the ceiling function ensures that sufficient material is obtained, which is particularly useful in scenarios where items are sold in whole units, such as bags of topsoil.

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