What is the volume of a…

Mathematics Questions

What is the volume of a pyramid in cubic inches, given the formula V = (1/3)Bh, where B is the area of the base and h is the height?

Short Answer

The volume of a pyramid can be calculated with the formula Volume = (1/3) √ó Base Area √ó Height. For a base of 8 and a height of 6, the volume calculates to 16 cubic inches after applying the formula.

Step-by-Step Solution

Step 1: Understand the Formula for Volume

The volume of a pyramid can be calculated using the formula: Volume = (1/3) √ó Base Area √ó Height. This means that the volume is one-third of the product of the base area and the height. Knowing this formula is crucial for solving pyramid volume problems.

Step 2: Identify the Base and Height

In this problem, the dimensions provided are: Base = 8 and Height = 6. Ensure that these values are correctly identified as they are critical for volume calculation. The base value usually refers to the shape of the base area of the pyramid, and the height is the vertical distance from the base to the apex.

Step 3: Perform the Calculation

To find the volume, use the values in the formula: Volume = (1/3) √ó 8 √ó 6. First, multiply the base and height: 8 √ó 6 = 48. Then, calculate one-third of 48 to determine the volume: (1/3) √ó 48 = 16 cubic inches. This gives you the final volume of the pyramid.

Related Concepts

Formula for volume

A mathematical equation used to calculate the volume of a shape, specifically in this case for a pyramid, defined as volume = (1/3) √ó base area √ó height.

Base area

The surface area of the base of the pyramid, which is the shape upon which it stands and is essential for determining the volume when multiplied by height.

Height

The vertical distance from the base of the pyramid to its apex, which is necessary for calculating the volume along with the base area.

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