Question

If each edge of a cube is doubled,

(i) How many times will its surface area increase?

(ii) How many times will its volume increase?​

Answer 1

Answer:

(i) let, the original edge of cube = a

given that edge is doubled,

therefore, new edge = 2a

surface area of original cube = 6 × (edge)²

= 6(a)²

=6a²

surface area of new cube = 6 × (edge)²

= 6(2a)²

= 6×4a²

= 4 × 6a²

= 4 × original surface area

therefore, new surface area will be 4 times original surface area.

(ii) let, the original edge of cube = a

given that edge is doubled,

therefore, new edge = 2a

volume of original cube = (edge)³

= a³

volume of new cube = (edge)³

= (2a)³

= 8a³

= 8 × a³

= 8 × original volume

therefore, new volume will be 8times original volume.