+13 The diagram shows a cylinder inside a cone on a horizontal base. The cone and the cylinder have the same vertical axis. The base of the cylinder lies on the base of the cone. The circumference of the top face of the cylinder touches the curved surface of the cone.
The height of the cone is 12cm and the radius of the base of the cone is 4cm.
d ^
d d / 12cm
d d
d d
dc c c c d
d c c d
d c c d
ddddccccccccddd d
4cm radius for cone
r cm radius for cyclinder
The cylinder has radius r cm and volume V cm3
Show that V = 12ʌr2 – 3ʌr3
+8 If we call as R(h), cone radius al a function of height h, then
R(h)= 4 -h/3 When cylider touchs the cone:
r = 4 - h/3 (1)
Area A of base cylinder is:
A =¶ *r2 and h by (1) is h = (12 -3r)
Cylinder volme is:
V = A *h = ¶ *r2 *(12 -3r)= ¶*(12 r2 - 3r3)
In your answer ¶ is missing
Regards
+33653 Another approach is to use similar triangles to get the height of the cylinder:
height of cylinder/(base radius of cone - radius of cylinder) = height of cone/base radius of cone
or
h/(4 - r) = 12/4
h = 3(4 - r) → 12 - 3r
V = pi*r^2*h → pi*(12r^2 - 3r^3)
or. V = 12pi*r^2 - 3pi*r^3
.
