Posted by Cassie on Sunday, February 17, 2013 at 11:52pm.
Could Answer c be 160 cm^3 and not 16 cm^3?
yes it is sorry.
The answer would then be C. 160 cm^3
The Volume of a cone is given by
V=(1/3)*pi*r^2*h
We know V= 540 cm^3 and that r=15 cm and can plug into the equation to find h.
I am going to leave the units off, but you should include it in your work.
540=(1/3)*pi*(15)^2*h
Solving for h gives
h=2.292 cm
Now a similar cone will have the same ratio
h1/r1 = h2/r2
(2.292 / 15) = (h2 / 10) and solve for h2.
h2 = 1.528 cm
Throw this into the Volume of a cone
V=(1/3)*pi*r^2*h
V=(1/3)*pi*(10)^2*(1.528) = 160 cm^3
simpler way:
the volume of 2 similar solids is proportional to the cube of their sides
V/540 = 10^3/15^3
V = 540(1000)/(3375) = 160
Thank you both...
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