# Algebra

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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...?

• Algebra -

Could Answer c be 160 cm^3 and not 16 cm^3?

• Algebra -

yes it is sorry.

• Algebra -

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

• Algebra -

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

• Algebra -

Thank you both...

• Algebra -

c i got 100%

• Algebra -

if you go to connexus academy the anwsers for the test are
D
B
C
A
A
C

• Algebra -

can someone give me the awnsers of the whole test i am in conections academy to.

• Algebra -

Yeah does anyone have the answers to the whole test