Question

(1) Two similar cuboids are shown below. One has a side length of 6cm and the other 12cm.

(a) Given the surface area of the smaller cuboid is 88cm² find the surface area of the larger cuboid.
(b) diven the volume of the larger cuboid is 384cm³ find the volume of the smaller cuboid.

Answer 1

The surface area of the larger cuboid is 352 88 cm²

The volume of the smaller cuboid is 48 cm³

How to find the surface area

We will need to find the scale factor first

bigger dimension * scale factor, k = smaller dimension

k = 6 / 12 = 1/2

K = 1/2

Hence from smaller to bigger we multiply by 2

To find the surface area of the larger cuboid using the scale factor we solve as follows

We are moving from smaller to bigger we multiply by 2. Also, since this is area which is square units we square the scale factor

= 88 cm² * 2²

= 88 cm² * 4

= 352 88 cm²

The volume of the smaller cuboid: Here, we move from bigger to smaller

k = 1/2

For cubic units we cube the k = (1/2)³ = 1/8

volume of the smaller cuboid = 1/8 * 384 cm³

volume of the smaller cuboid = 48 cm³