Maria has a cube-shaped box that measures 9 inches along each edge. Can she fit 1,000 1-cubic-inch cubes inside the box?

Question

UpStudy AI · Accepted Answer

To determine whether Maria can fit **1,000** 1-cubic-inch cubes inside her cube-shaped box, let's perform some calculations:

1. **Calculate the Volume of the Box:**
   
   Since the box is cube-shaped with each edge measuring **9 inches**, its volume (**V_box**) is:
   
   $$
   V_{\text{box}} = \text{edge length}^3 = 9 \, \text{in} \times 9 \, \text{in} \times 9 \, \text{in} = 729 \, \text{cubic inches}
   $$

2. **Calculate the Total Volume of the 1-Cubic-Inch Cubes:**
   
   Each small cube has a volume of **1 cubic inch**, so **1,000** such cubes would have a total volume (**V_cubes**) of:
   
   $$
   V_{\text{cubes}} = 1,000 \times 1 \, \text{cubic inch} = 1,000 \, \text{cubic inches}
   $$

3. **Compare the Volumes:**
   
   - **Box Volume:** 729 cubic inches
   - **Total Cubes Volume:** 1,000 cubic inches
   
   Since **1,000 cubic inches** (the volume needed for the cubes) **exceeds** the box's capacity of **729 cubic inches**, Maria **cannot** fit all **1,000** 1-cubic-inch cubes inside the box.

**Conclusion:**  
Maria cannot fit 1,000 1-cubic-inch cubes inside her 9-inch cube-shaped box because the total volume of the cubes exceeds the box's volume.
Maria cannot fit 1,000 1-cubic-inch cubes inside her 9-inch cube-shaped box because the total volume of the cubes (1,000 cubic inches) is larger than the box's volume (729 cubic inches).

Maria has a cube-shaped box that measures 9 inches along each edge. Can she fit 1,000 1-cubic-inch cubes inside the box?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Geometry Questions