Question

Cuboid A has a dimension of 7cm x 6cm x 5cm. Cuboid B has a dimension of 10cm x 9cm x 3cm. Work out the surface area to volume ratios of both cuboids and determine which one has a higher ratio. Give your ratio in its simplest form.​

Answer 1

Cuboid A:

S = 2((7(6) + 6(5) + 7(5)) = 2(42 + 30 + 35)

= 2(107) = 214 cm²

V = 7(6)(5) = 42(5) = 210 cm³

S:V = 214:210 = 107:105 = about 1.02:1

Cuboid B:

S = 2((10(9) + 9(3) + 10(3)) = 2(90 + 27 + 30)

= 2(147) = 294 cm²

V = 10(9)(3) = 10(27) = 270 cm³

S:V = 294:270 = 49:45 = about 1.09:1

Cuboid B has a higher S:V ratio.