NZ Level 7 (NZC) Level 2 (NCEA) Applications of Power Functions

## Interactive practice questions

For a cube with sides of length $x$x, the volume is given by the formula $V=x^3$V=x3 and the surface area is given by the formula $S=6x^2$S=6x2.

a

Find the volume of a cube whose sides are $3$3 m:

b

Find the surface area of a cube whose sides are $6$6 cm:

Easy
Approx a minute

The surface area of skin on a human body can be approximated by the equation $A=0.007184h^{0.725}w^{0.425}$A=0.007184h0.725w0.425, where $A$A is the skin area in m2 of a person who is $h$h cm tall, and weighs $w$w kg.

In total, $\frac{2}{5}$25 of Britney’s skin is covered in sun spots and sun damage.

When swimming underwater, the pressure $P$P (Newtons/$m^2$m2) of the water on your body varies directly with the depth $d$d (metres) at which you are swimming. At $2$2 metres, the pressure of the water is about $20188$20188 Newtons /$m^2$m2 (We are ignoring atmospheric pressure in this example).

In wakeboarding, power is generated by the engine of the boat to create a wake in the rider’s path. The amount of power ($A$A horsepower) used to generate the wake is directly proportional to the $6$6th power of the speed ($v$v knots) of the boat. A particular boat’s design is such that it produces $67765824$67765824 horsepower to generate the wake when travelling at $14$14 knots.

### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems