Let's solve each problem step by step.
---
Problem 1: What is the volume of this box made up of 1 cm cubes?
####
Solution:
The box is composed of small cubes, each with a side length of 1 cm. To find the volume, we need to count the number of these 1 cm cubes in the box.
- The box has
3 layers (height).
- Each layer has
4 rows.
- Each row has
2 cubes.
So, the total number of cubes is:
\[
\text{Total cubes} = \text{Layers} \times \text{Rows per layer} \times \text{Cubes per row}
\]
\[
\text{Total cubes} = 3 \times 4 \times 2 = 24
\]
Since each cube has a volume of \(1 \, \text{cm}^3\), the total volume of the box is:
\[
\text{Volume} = 24 \, \text{cm}^3
\]
####
Answer:
\[
\boxed{a}
\]
---
Problem 2: What is the volume of a crate measuring 1 m by 2 m by 1.5 m?
####
Solution:
The volume of a rectangular prism (crate) is given by the formula:
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
Here:
- Length = 1 m
- Width = 2 m
- Height = 1.5 m
Substitute these values into the formula:
\[
\text{Volume} = 1 \, \text{m} \times 2 \, \text{m} \times 1.5 \, \text{m} = 3 \, \text{m}^3
\]
####
Answer:
\[
\boxed{b}
\]
---
Problem 3: The area of a square is 36 cm². What is the length of its base?
####
Solution:
The area of a square is given by the formula:
\[
\text{Area} = \text{Side}^2
\]
Here, the area is \(36 \, \text{cm}^2\). Let the side length be \(s\). Then:
\[
s^2 = 36
\]
To find \(s\), take the square root of both sides:
\[
s = \sqrt{36} = 6 \, \text{cm}
\]
####
Answer:
\[
\boxed{a}
\]
---
Problem 4: A rectangular field has length 80 m. What is its width if the perimeter is 240 m?
####
Solution:
The perimeter of a rectangle is given by the formula:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
\]
Here:
- Perimeter = 240 m
- Length = 80 m
- Width = \(w\) (unknown)
Substitute the known values into the formula:
\[
240 = 2 \times (80 + w)
\]
Divide both sides by 2:
\[
120 = 80 + w
\]
Solve for \(w\):
\[
w = 120 - 80 = 40 \, \text{m}
\]
####
Answer:
\[
\boxed{b}
\]
---
Final Answers:
1. \(\boxed{a}\)
2. \(\boxed{b}\)
3. \(\boxed{a}\)
4. \(\boxed{b}\)
Parent Tip: Review the logic above to help your child master the concept of area and perimeter worksheet 6th grade.