Asked by Cassie

A cone has a radius of 15 cm and a volume of 540 cm3. Find the volume of a similar cone with a radius of 10 cm.

A. 54 cm^3
B. 240 cm^3
C. 16 cm^3
D. 360 cm^3

I think its D but by the process of elimination...don't know how to figure it out really...?
Answered by Jeff
Could Answer c be 160 cm^3 and not 16 cm^3?
Answered by Cassie
yes it is sorry.
Answered by Jeff
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
Answered by Reiny
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
Answered by Cassie
Thank you both...
Answered by Monkey D. Luffy
c i got 100%
Answered by anwsers for the test
if you go to connexus academy the anwsers for the test are
D
B
C
A
A
C
Answered by Hi
can someone give me the awnsers of the whole test i am in conections academy to.
Answered by Unknown
Yeah does anyone have the answers to the whole test

Answered by joss
54 a
Answered by Black Butler 🌹🤫🧐😈 -_-||
There are so many questions like this and none of then that I have found have the answers.

😟😔 （ˇˍˇ）
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