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India
Class XI

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
1min

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.

Easy
3min

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).

Easy
3min

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.

Easy
5min
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Outcomes

11.SF.RF.2

Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.

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