Find the volume, lateral surface area and the total surface area of a cube each of whose edges measures:
(i) 7 m (ii) 5.6 cm (iii) 8 dm 5 cm
(i) We have,
Length of the edge of the cube = a = 7 cm
We know that,
Volume of cube = a3 = 73 = 343 m3
Also,
Lateral surface area of the cube = 4a2
= 4 × 7 × 7
= 196 m2
Total surface area of the cube = 6a2
= 6 × 7 × 7
= 294 m2
(ii) We have,
Length of the edge of the cube = a = 5.6 cm
We know that,
Volume of cube = a3 = (5.6)3 = 175.616 cm3
Also,
Lateral surface area of the cube = 4a2
= 4 × 5.6 × 5.6
= 125.44 cm2
Total surface area of the cube = 6a2
= 6 × 5.6 × 5.6
= 188.16 cm2
(iii) We have,
Length of the edge of the cube = a = 8 dm 5 cm = 85 cm
We know that,
Volume of cube = a3 = 853 = 614125 cm3
Also,
Lateral surface area of the cube = 4a2
= 4 × 85 × 85
= 28900 cm2
Total surface area of the cube = 6a2
= 6 × 85 × 85
= 43350 cm2