The approximate volume of a human eye is 6.5 cm³. The volume of a laboratory model (excluding base and stand) of the human eye is 1404 cm³.

(a) State whether the scale factor k is less than, equals to or greater than 1.

(b) Calculate the:

(i) value of k

(ii) diameter of the human eye if the radius of the model is 7.2 cm.

(iii) the external surface area of the human eye if the surface area of the model is 651.6 cm².

(a) Scale factor is greater than 1 as volume of model is greater than the original eye.

(b)

(i) By formula,

$\Rightarrow k^3 = \dfrac{\text{Volume of model}}{\text{Volume of original human eye}} \\[1em] \Rightarrow k^3 = \dfrac{1404}{6.5} \\[1em] \Rightarrow k^3 = \dfrac{216}{1} \\[1em] \Rightarrow k^3 = 6^3 \\[1em] \Rightarrow k = 6.$

Hence, scale factor (k) = 6.

(ii) By formula,

$\Rightarrow k = \dfrac{\text{Radius of model}}{\text{Radius of human eye}} \\[1em] \Rightarrow 6 = \dfrac{7.2}{\text{Radius of human eye}} \\[1em] \Rightarrow \text{Radius of human eye} = \dfrac{7.2}{6} = 1.2 \text{ cm}$

Diameter of human eye = 1.2 × 2 = 2.4 cm

Hence, diameter of human eye = 2.4 cm.

(iii) By formula,

$\Rightarrow k^2 = \dfrac{\text{Surface area of model}}{\text{Surface area of human eye}} \\[1em] \Rightarrow 6^2 = \dfrac{651.6}{\text{Surface area of human eye}} \\[1em] \Rightarrow \text{Surface area of human eye} = \dfrac{651.6}{6^2} \\[1em] \Rightarrow \text{Surface area of human eye} = \dfrac{651.6}{36} = 18.1 \text{ cm}^2.$

Hence, surface area of human eye = 18.1 cm².