SOLUTION: a conical block of silver has a height of 16c, and a base radius of 12cm.how many coins 1/6cm thick and 1 1/2 cm in diameter can be made by melting the silver? The answer at the

Algebra ->  Volume -> SOLUTION: a conical block of silver has a height of 16c, and a base radius of 12cm.how many coins 1/6cm thick and 1 1/2 cm in diameter can be made by melting the silver? The answer at the      Log On


   

Question 861750: a conical block of silver has a height of 16c, and a base radius of 12cm.how many coins 1/6cm thick and 1 1/2 cm in diameter can be made by melting the silver?
The answer at the back of the book is 8192
please explain in detail and give the solution with steps.
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of cone = 1/3 * pi * r^2*h
=1/3 *pi*12^2*16
=768 pi

Volume of coin = pi r^2 h
=pi*(3/4)^2*(1/6)
=0.09 pi
Number of coins = Volume of cone/volume of coin
=768 pi/0.09 pi
= 8192 coins

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the silver in the cone form is %281%2F3%29%2A16%2Api%2A12%5E2, and the volume of one coin is %281%2F6%29%2Api%2A%28%281%261%2F2%29%2F2%29%5E2.

Simplify each of those volumes.
The cone of silver: pi%2816%29%281%2F3%29%2812%2A3%2A4%29=pi%2A16%2A12%2A4;
Coin of silver: .

How many coin volumes are in one cone volume?
%28pi%2A16%2A12%2A4%29%2F%28pi%2A%283%2F32%29%29
Continue to simplify this rational expression. What does it become?

%2816%2A12%2A4%2A32%29%2F%283%29
16%2A4%2A4%2A32
16%2A16%2A32
256%2A32
highlight%288192%29