I'll solve these three volume problems step by step.
Problem 1: Cube with side 5 cm
For a cube, all sides are equal. The formula for volume is:
Volume = side × side × side (or side³)
Volume = 5 cm × 5 cm × 5 cm
Volume = 25 cm² × 5 cm
Volume = 125 cm³
Problem 2: Rectangular prism with dimensions 6 cm × 6 cm × 11 cm
For a rectangular prism, the formula for volume is:
Volume = length × width × height
Volume = 6 cm × 6 cm × 11 cm
Volume = 36 cm² × 11 cm
Volume = 396 cm³
Let me verify: 6 × 6 = 36, and 36 × 11 = 36 × 10 + 36 × 1 = 360 + 36 = 396 ✓
Problem 3: Triangular prism
This is a triangular prism. To find its volume:
- First, find the area of the triangular base
- Then multiply by the length of the prism
The triangle has:
- Base = 8 cm
- Height = 6 cm (the perpendicular height shown)
Area of triangle = (base × height) ÷ 2
Area = (8 cm × 6 cm) ÷ 2
Area = 48 cm² ÷ 2
Area = 24 cm²
Now multiply by the length of the prism (12 cm):
Volume = Area of base × length
Volume = 24 cm² × 12 cm
Volume = 288 cm³
Let me verify: 24 × 12 = 24 × 10 + 24 × 2 = 240 + 48 = 288 ✓
Final Answer:
1) 125 cm³
2) 396 cm³
3) 288 cm³
Parent Tip: Review the logic above to help your child master the concept of 7th grade surface area worksheet.