https://file.aiquickdraw.com/mathbot/file/1726404433147fwn85nkg.jpg

Let's solve this problem step by step:

### Problem Breakdown:
1. **The cake's dimensions**:
   - Width: 15 cm
   - Length: 20 cm
   - The total area of the cake = \( 15 \, \text{cm} \times 20 \, \text{cm} = 300 \, \text{cm}^2 \)

2. **The cake is divided into 24 pieces**:
   - Each piece is a square. The total number of pieces = 24.
   - The area of each piece = \( \frac{300 \, \text{cm}^2}{24} = 12.5 \, \text{cm}^2 \)

3. **\(\frac{3}{4}\) of the cake is eaten**:
   - \(\frac{3}{4}\) of the total number of pieces are eaten.
   - Number of pieces eaten = \( \frac{3}{4} \times 24 = 18 \)
   - Number of pieces remaining = \( 24 - 18 = 6 \)

4. **Area of the remaining part**:
   - Each remaining piece has an area of 12.5 cm².
   - Total area of the remaining cake = \( 6 \times 12.5 \, \text{cm}^2 = 75 \, \text{cm}^2 \)

### Conclusion:
The total area of the remaining part of the cake is **75 cm²**, which corresponds to **Option D (7.5 × 10)**.

---

Would you like more details or have any other questions?

### Related Questions:
1. What would be the area of the cake if it were divided into 30 pieces?
2. How many pieces would be left if \(\frac{1}{2}\) of the cake were eaten instead of \(\frac{3}{4}\)?
3. What is the area of one piece if the total cake area was doubled, but it was still divided into 24 pieces?
4. How would the problem change if the width of the cake were 10 cm instead of 15 cm?
5. How do you calculate the area of one piece if the cake is cut into triangles instead of squares?

### Tip:
Always double-check your unit conversions and fractional calculations when solving area problems.

Sumayyah bought a rectangular cake with a width of 15 cm and a length of 20 cm for her mother’s birthday. She cut the entire cake into 24 square-shaped pieces. 3/4 of the cake has been eaten. Calculate the area, in cm², of the remaining part of the cake.

Learn how to calculate the remaining area of a rectangular cake after 3/4 of it is eaten. This problem covers key geometric concepts, including the area of a rectangle and fraction calculations. 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