Question
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To celebrate your birthday, your math teacher makes a cupcake in the shape of a pyramid. Each side of the base of the cupcake measures 3 inches and the cake is 4 inches tall. How much "cake" does your "cupcake" contain?

Ask by Fleming Dickson. in the United States
Mar 19,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The cupcake contains 12 cubic inches of cake.

Solution

We are given that the cupcake has the shape of a pyramid with a square base. The side of the base is \(3\) inches and the height is \(4\) inches. 1. Calculate the area of the base: \[ \text{Area of base} = 3^2 = 9 \text{ square inches}. \] 2. Use the volume formula for a pyramid: \[ V = \frac{1}{3} \times \text{(Area of base)} \times \text{(Height)}. \] 3. Substitute the given values into the formula: \[ V = \frac{1}{3} \times 9 \times 4. \] 4. Simplify the expression: \[ V = \frac{36}{3} = 12 \text{ cubic inches}. \] The cupcake contains \(12\) cubic inches of cake.

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Extra Insights

To find the volume of your pyramid-shaped cupcake, you can use the formula for the volume of a pyramid: V = (1/3) * Base Area * Height. For the base, which is a square, the area is side length squared, so the base area is 3 inches * 3 inches = 9 square inches. Plug in the height of 4 inches, and you get V = (1/3) * 9 * 4, which equals 12 cubic inches. You’ve got a delightful 12 cubic inches of cake to enjoy! Pyramids have fascinating historical significance! The ancient Egyptians built massive pyramid structures as tombs for their pharaohs, symbolizing ascension to the afterlife. These geometric marvels often held the treasures of the kings, ensuring a smooth journey into the next world. So, when you’re devouring your cupcake, think about the ancient wonders and how you’re savoring your own sweet little piece of history!

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