SOLUTION: A frustum of a solid cone has height 30cm,radius 10cm and 15cm.Determine the: (i) height of original cone (ii) volume of the frustum (iii) total surface area of the frustum

Algebra ->  Formulas -> SOLUTION: A frustum of a solid cone has height 30cm,radius 10cm and 15cm.Determine the: (i) height of original cone (ii) volume of the frustum (iii) total surface area of the frustum       Log On


   

Question 1040485: A frustum of a solid cone has height 30cm,radius 10cm and 15cm.Determine the:
(i) height of original cone
(ii) volume of the frustum
(iii) total surface area of the frustum
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
VOLUME: %281%2F3%29pi%2Ah%28R%5E2%2BrR%2Br%5E2%29, if r is the small radius and R is the large radius.


HEIGHT of ORIGINAL CONE: Imagine a cross section through the center axis. Orient this cross section so that the short base is along x-axis and long base is parallel to but above the x-axis. Position this on cartesian system so that the slanted side segment is in quadrant 1, and center is at x=0. The graph of the endpoints for the slanted segment is the two points, (10,0) and (15,30).

What is the equation for the line containing those two point? What is the y-axis intercept?
..... Do you see how to finish finding the height of the original cone?
(You really do not need to make the graph. Doing it might help to visualize the process.)

SURFACE AREA:
Formula is pi%28R%5B1%5D%2BR%5B2%5D%29sqrt%28%28R%5B1%5D-R%5B2%5D%29%5E2%2Bh%5E2%29
(Found in wikipedia)