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3 of 3 (b) Find the midpoint

`D`

of

`AC`

. (c) Write down the equation of the circle that has

`AC`

as diameter. 4.7 Find the maximum vertical distance between the graphs of

`f`

and

`g`

on the interval

`xin[0;6]`

. Hint: First find an expression which defines this vertical distance. 4.8 Use the graphs of

`f`

and

`g`

(not calculations) to solve

`f(x)*g(x)>=0`

`30`

Question 5 A glass tank is

`25cm`

long,

`20cm`

wide,

`30cm`

high and contains water. The surface of the water is 5

`cm`

below the top of the tank. After a solid metal spherical ball

`B_(1)`

has carefully been placed into the tank, the surface of the water is

`3cm`

below the top of the tank. (The formula for the volume of a sphere (ball) is

`(4)/(3)\pi r^(3)`

.) 5.1 Calculate the volume of the ball. Hint: The volume of the ball is equal to the volume of water displaced by the ball. 5.2 Calculate the radius of the ball. Leave your answer in terms of

`\pi `

and a surd if necessary. 5.3 Suppose the radius of a second solid metal ball,

`B_(2)`

, is half the radius of ball

`B_(1)`

. Suppose ball

`B_(2)`

was put into the tank of water instead of ball

`B_(1)`

. Would the surface of the water be

`4cm`

below the top of the tank? Explain your answer. TOTAL:

`100`