Matn ill WAR1 Sector 22 Right Cone Shown below is a right co

Matn ill WAR1 Sector: 22. Right Cone: Shown below is a right cone with aslant height of12 cm. Complete the following. 12 cm (a) Determine trig equations to model the radius, r and height, h in terms of 6. r(0) h(0) Volume of a Cone: V mr2h (6) (c) If 0 20, what is the volume of the cone? v(20) (d) With your graphing calculator, graph the function VC6). Use the graph to determine the angle that will maximize the volume. Max Volume (e) Using your graphing calculator, determine the angles of 0 that will have a volume of 500 cm2.

Solution

22.a . In the given figure

sin theta=r(theta)/ hypotenuse

r(theta)=12 sin theta

cos theta=h(theta)/hypotenuse

h(theta)=12 cos theta

b. Volume of cone is given by

V=(1/3)pi*r²h

V(theta)=(1/3)pi* (12 sin theta)²(12 cos theta)

            = 576 (sin theta)²cos theta

c. theta =20 degree

V(20)= 576(sin 20)²cos 20= 63.32cm²