the volume of a cube is 125m^3 find its total surface area lateral surface area and the length of the longest rod that can be fitted into it
Answers
Answered by
2
Answer:
Total surface area 150 m²
Lateral surface area 100 m²
Longest rod 5√3 m ≈ 8.66 m
Step-by-step explanation:
Volume = side³ = 125 m³ => side = 5 m
Area of one face is then
Face area = side² = 25 m²
Total surface is made of six faces:
Total SA = 6 × face area = 6 × 25 m² = 150 m²
Lateral surface is made of four walls / faces:
Lateral SA = 4 × face area = 4 × 25 m² = 100 m²
The longest rod that will fit goes from one corner to the opposite corner. The distance, d, is given by (generalization of) Pythagoras' Theorem:
d = √ ( 5² + 5² + 5² ) = √ ( 3 × 5² ) = 5√3 m ≈ 8.66 m.
Similar questions