Calculating Cuboid Base Area from Volume and Height

This problem involves finding the area of the base of a cuboid when its volume and height are known. A cuboid is a three-dimensional shape with six rectangular faces. The volume of a cuboid is calculated by multiplying its length, width, and height. The base of a cuboid is typically one of its rectangular faces, and its area is calculated by multiplying its length and width.

The relationship between the volume, base area, and height of a cuboid is given by the formula:

\(\text{Volume} = \text{Area of Base} \times \text{Height}\)

We are given the following information:

• Volume of the cuboid = 4800 cm³
• Height of the cuboid = 20 cm

We need to find the area of the base of the cuboid. We can rearrange the formula for the volume of a cuboid to solve for the Area of Base:

\(\text{Area of Base} = \frac{\text{Volume}}{\text{Height}}\)

Step-by-Step Calculation

Now, let's substitute the given values into the rearranged formula:

\(\text{Area of Base} = \frac{4800 \text{ cm}^3}{20 \text{ cm}}\)

Performing the division:

\(\text{Area of Base} = 240 \text{ cm}^2\)

Therefore, the area of the base of the cuboid is 240 cm². The unit for area is square centimeters (cm²) because we divided volume (cm³) by height (cm), resulting in cm³ / cm = cm².

Let's verify this with the original formula:

Volume = Area of Base \(\times\) Height

Volume = 240 cm² \(\times\) 20 cm

Volume = 4800 cm³

This matches the given volume, confirming our calculation for the base area is correct.

Summary of Cuboid Dimensions

The area of the base of the cuboid is 240 cm².

Cuboid Volume and Area Revision

Let's quickly revise the key concepts related to cuboids, volume, and area that were used in solving this problem.

• Cuboid: A solid three-dimensional shape with six rectangular faces at right angles to each other.
• Volume: The amount of space occupied by a three-dimensional object. For a cuboid with length \(l\), width \(w\), and height \(h\), the volume \(V\) is given by \(V = l \times w \times h\).
• Area of Base: The area of the bottom face of the cuboid. If the length is \(l\) and the width is \(w\), the base area \(A_{\text{base}}\) is \(A_{\text{base}} = l \times w\).
• From these definitions, we can see that \(V = (l \times w) \times h = A_{\text{base}} \times h\), which is the formula we used.

Additional Information on Cuboid Properties

Understanding the different properties of a cuboid is important for solving geometry problems. Here is some additional information:

• Surface Area: The total area of all six faces of the cuboid. For a cuboid with length \(l\), width \(w\), and height \(h\), the total surface area is \(2(lw + lh + wh)\).
• Faces, Edges, and Vertices: A cuboid has 6 faces (rectangles), 12 edges (line segments where faces meet), and 8 vertices (points where edges meet).
• Units: It is crucial to use consistent units. Volume is measured in cubic units (like cm³), area in square units (like cm²), and length/height in linear units (like cm).

Knowing the relationship between volume, base area, and height allows us to calculate any one of these values if the other two are known, as demonstrated in this problem.