A cubed shape cake has a volume of 1080cm³. The cake is cut into several small cubed shape pieces with an edge length of 6 cm. Find the number of pieces of cake that can be cut

To find the number of smaller cubed pieces that can be cut from the larger cubed-shaped cake, we can follow these steps:

1. **Determine the Edge Length of the Larger Cube:**

   Since the volume of the larger cube is given, we can find its edge length using the formula for the volume of a cube:

   \[
   V = a^3
   \]

   where \( V \) is the volume and \( a \) is the edge length of the cube. We are given:

   \[
   1080 \, \text{cm}^3 = a^3
   \]

   Solving for \( a \):

   \[
   a = \sqrt[3]{1080}
   \]

   Let's calculate \( a \):

   \[
   a \approx \sqrt[3]{1080} \approx 10.32 \, \text{cm}
   \]

   The edge length of the larger cube is approximately \( 10.32 \, \text{cm} \).

2. **Volume of Smaller Cubes:**

   Each smaller cube has an edge length of 6 cm. The volume of each smaller cube is:

   \[
   v = 6^3 = 216 \, \text{cm}^3
   \]

3. **Determine the Number of Smaller Cubes:**

   To find the number of smaller cubes that can be cut from the larger cube, we divide the volume of the larger cube by the volume of each smaller cube:

   \[
   \text{Number of smaller cubes} = \frac{1080 \, \text{cm}^3}{216 \, \text{cm}^3}
   \]

   Calculating this gives:

   \[
   \text{Number of smaller cubes} = 5
   \]

Therefore, the larger cake can be cut into **5 smaller cubes** each with an edge length of 6 cm.

Would you like any additional details or have any questions? Here are some related questions you might find interesting:

1. What is the volume of a cube with an edge length of 8 cm?
2. How would the number of pieces change if the smaller cubes had an edge length of 5 cm?
3. If the larger cube had a different volume, how would you calculate the number of smaller cubes?
4. What would be the volume of a sphere with a radius equal to the edge length of the smaller cubes?
5. Can you find the surface area of one of the smaller cubes?
6. How does the volume change if each dimension of a cube is doubled?
7. If the larger cube is cut into pieces with an edge length of 3 cm, how many pieces would that make?
8. What happens to the volume if the side length of a cube is halved?

**Tip:** When dealing with geometric shapes, remember that volume scales with the cube of the dimensions, meaning small changes in size can lead to large changes in volume.

Learn how to calculate the number of smaller cubes that can be cut from a larger cake with a volume of 1080cm³. Detailed step-by-step solution using the volume formula for a cube and division. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation