Math Problem Statement

For the upcoming holiday season, Dorothy wants to mold 20 bars of chocolate into tiny pyramids. Each bar of chocolate contains 6 cubic inches of chocolate. Dorothy plans to make chocolate pyramids with a square base of 1 square inch and a height of 2 inches. What is the largest number of pyramids she can make from the 20 bars of chocolate?

Solution

To determine how many chocolate pyramids Dorothy can make, we need to follow these steps:

  1. Calculate the total volume of chocolate Dorothy has:

    • Each bar of chocolate contains 6 cubic inches.
    • Dorothy has 20 bars of chocolate. Total volume of chocolate=20×6=120 cubic inches\text{Total volume of chocolate} = 20 \times 6 = 120 \text{ cubic inches}
  2. Calculate the volume of one chocolate pyramid:

    • The formula for the volume VV of a pyramid with a square base is: V=13×base area×heightV = \frac{1}{3} \times \text{base area} \times \text{height}
    • The base area is 1 square inch, and the height is 2 inches. V=13×1×2=23 cubic inchesV = \frac{1}{3} \times 1 \times 2 = \frac{2}{3} \text{ cubic inches}
  3. Determine the number of pyramids that can be made:

    • We need to divide the total volume of chocolate by the volume of one pyramid. Number of pyramids=120 cubic inches23 cubic inches/pyramid=120×32=180\text{Number of pyramids} = \frac{120 \text{ cubic inches}}{\frac{2}{3} \text{ cubic inches/pyramid}} = 120 \times \frac{3}{2} = 180

Therefore, the largest number of pyramids Dorothy can make from the 20 bars of chocolate is:

180\boxed{180}

Would you like details or have any questions?

Here are 5 numbered questions you may consider:

  1. How do you calculate the volume of a rectangular prism?
  2. What is the formula for the surface area of a pyramid?
  3. How do you determine the volume of a cylinder?
  4. What are the properties of similar pyramids?
  5. How do you find the height of a pyramid if the volume and base area are known?

Tip: Always verify the units of measurement when solving geometry problems to ensure consistency and accuracy.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume calculations
Pyramids

Formulas

Volume of a pyramid formula: V = (1/3) * base area * height

Theorems

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Suitable Grade Level

Grades 7-9