Question

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

Answer 1

(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