A bookend that weights 0.24 pounds is shaped like a pyramid with square base. How many pounds does a larger similar pyramid-shaped booked weigh if it is made of the same material and each corresponding dimensions is `2(1)/(2)` times as large?

Answer

To solve the problem, we need to find the weight of a larger similar pyramid-shaped bookend given that its dimensions are scaled by a factor of \(2.5\) times the original pyramid.

### Step-by-step Solution:

1. **Understand the relationship between volume and weight:**
The weight (mass) of an object is directly proportional to its volume when the density remains constant. Therefore, we can write:
\[ \frac{m_1}{V_1} = \frac{m_2}{V_2} \]
where \(m_1\) and \(m_2\) are the weights of the original and larger pyramids, and \(V_1\) and \(V_2\) are their respective volumes.

2. **Calculate the volume of the original pyramid:**
The volume \(V\) of a pyramid with a square base can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For the original pyramid, if the side of the base is \(a\) and the height is \(h\), then:
\[ V_1 = \frac{1}{3} \times a^2 \times h \]

3. **Calculate the volume of the larger pyramid:**
The dimensions of the larger pyramid are \(2.5\) times those of the original. Therefore, the side of the base becomes \(2.5a\) and the height becomes \(2.5h\). The volume of the larger pyramid is:
\[ V_2 = \frac{1}{3} \times (2.5a)^2 \times (2.5h) = \frac{1}{3} \times 6.25a^2 \times 2.5h = \frac{1}{3} \times 15.625a^2 \times h \]

4. **Relate the volumes:**
Now we can express the ratio of the volumes:
\[ \frac{V_2}{V_1} = \frac{\frac{1}{3} \times 15.625a^2 \times h}{\frac{1}{3} \times a^2 \times h} = 15.625 \]

5. **Find the weight of the larger pyramid:**
Using the relationship between weights and volumes:
\[ \frac{m_2}{m_1} = \frac{V_2}{V_1} \]
Substituting the known values:
\[ m_2 = m_1 \times \frac{V_2}{V_1} = 0.24 \times 15.625 \]

6. **Calculate \(m_2\):**
\[ m_2 = 0.24 \times 15.625 = 3.75 \text{ pounds} \]

### Final Answer:
The weight of the larger similar pyramid-shaped bookend is **3.75 pounds**.