Question

A cuboid is 3 cm by 4 cm by 7 cm. Explain whether doubling all of the dimensions would double the surface area? ​

Answer 1

doubling the dimensions would change the dimensions to 9 cm by 8 cm by 14 cm
the SA of a cuboid is 2(lh + bh + lb) meaning the original cuboid would have an SA of:
2[(3)(4) + (4)(7) + (3)(7))]
= 2[(12) + (28) + (21)]
= 2 x 61 = 122 cm squared

the other cuboid would have an SA of:
2[(9)(8) + (8)(14) + (9)(14)]
= 2[ 72 + 112 + 126 ]
= 2 x 310 = 620 cm squared

hence doubling the dimensions would not double the surface area.