Question

the volumes of two mathematically similar objects ar in the ratio 8:125. the surface area of the smaller solid is 24cm squared. find the surface area of the bigger object

Answer 1

The surface area of the bigger object is 150cm³

Similar shapes are shapes that that have equal corresponding angles and equal corresponding sides ratio.

The ratio of the corresponding sides are equal and this ratios are called scale factor.

area scale factor = (linear scale factor )²

scale factor is the cube root of volume scale factor

linear scale factor =

`\sqrt[3]{(8)/(125) }`

= 2/5

area scale factor =( 2/5)² = 4/25

area of bigger solid is x

24/x = 4/25

4x = 600

x = 600/4

x = 150cm³

Therefore, area of the bigger solid is 150cm³