http://www.neonlightssigns.info/cone-top/
Cone Top
The cone is cut by a plane parallel to its base. The small cone on top is similar to the large cone. the ratio
of the slant heights of the cone is 1:2.
Find the ratio indicated.
a)the surface area of the large cone to that of the small cone; the volume of the large cone to that of the small cone.
b)the surface area of the frustum to that of the large cone; to that of the small cone.
c)the volume of the frustum to that of the large cone; to that of the small cone.
If the slant heights are 1:2, then :
Slant height of small cone = Slant height of frustum
Let R = radius of large cone , H = height of large cone.
Let r = radius of small cone , h = height of small cone.
By ratios in similar triangles, we have : 1/(2r) = 2/2R,
which gives : r =R/2.
Also, we have : h = H/2
General Formulae :
Lateral surface area of a cone = πRL (L = lateral length)
Volume of a cone = πR^2H/3
(a)(i) Lat. surface area of large cone = πR2
Lat. surface area of small cone = π(R/2)1
Ratio = πR2 / [π(R/2)1] = 4
(a)(ii) Volume of large cone = πR^2H/3
Volume of small cone = π(R/2)^2(H/2)/3 = πR^2H/24
Ratio = (πR^2H/3) / ( πR^2H/24) = 8
(b)(i) Lat. surface area of frustum =
Lat. S.A. of large cone - Lat. S.A. of small cone
= 2πR - πR/2 = 3πR/2
Ratio = (3πR/2) / (2πR) = 3/4
(b)(ii) Ratio = (3πR/2) / (πR/2) = 3
(c)(i) Volume of frustum =
Volume of large cone - Volume of small cone
= πR^2H/3 - πR^2H/24 = 7πR^2H/24
Ratio = (7πR^2H/24) / (πR^2H/3) = 7/8
(c)(ii) Ratio = (7πR^2H/24) / (πR^2H/24) = 7
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Performance and working principle of Cone crusher
Cone crusher performance:
Used cone crusher, the crushing hardness f ? 5-16 Platts variety of minerals and rocks. Crusher structure from the frame body, adjust the device, adjusting the sets, broken cone, transmission and eccentric sets and other major parts and electrical, lubrication and other auxiliary components. PY Series Cone Crusher broken sub-coarse, medium broken cone crusher and crushing three kinds of cone crusher, crusher of this series is suitable for crushing all kinds of above average hardness of ore and rock. Crushing chamber type of ore used by the decision, the standard type used in the pieces; medium applicable to small and fragmented; short head type apply to broken bits. According to the different needs of customers purchase.
Cone crusher working principle:
Cone crusher work, the motor rotation through the belt pulley or coupling, transmission shaft and Cone crusher eccentric sleeve to force the Department of dynamic fixed-point next week to spin around the pendulum movement. Broken cone so close to another of the broken wall sometimes and sometimes leave the solid-mounted to adjust the rolling bearing acetabular wall surface, so that ore constantly under attack in the crushing cavity, pressing and bending role of the realization of the ore crushing. Motor-driven through the bevel gear sets eccentric rotation, so broken for rotary cone pendulum movement. Cone sometimes broken and sometimes also the left near the fixed cone, complete crushing and marker. Support sleeve and frame body junction pressed by spring, when the crushing machine can not be broken into pieces of scrap metal and other objects, the springs that generate compression deformation, emission of foreign body, to achieve insurance, to prevent damage to the machine.
Cone crusher in the foreign body can not break through the crushing chamber, or for some reason, overloading the machine, the cone crusher spring insurance system to achieve insurance, cone crusher increase of discharge mouth. Foreign matter from the cone crusher chamber discharges, such as foreign body stuck in the row of clear-cavity system ore can be used to make row mine continues to increase, so that foreign matter discharge cone crusher chamber. Cone crusher in the spring under the effect of discharge port auto-reset, cone crusher machine to resume normal work. Crushing cavity surface paved with wear-resistant high manganese steel liner. Pai mine mouth size of the used hydraulic or manual adjustment.
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Crusher, cone crusher, Cone crusher
