Geometry help? Volume of a cone.
The volume of a cone is 1014𝜋 𝑖𝑛^3. The height of the cone is 18 𝑖𝑛.
What is the exact circumference of the base of the cone? Do NOT round at any point!
The volume of a cone is 1014𝜋 𝑖𝑛^3. The height of the cone is 18 𝑖𝑛.
What is the exact circumference of the base of the cone? Do NOT round at any point!
2 Answers
Explanation:
"to find circumference we require to know the radius r"
"using the following formulae"
•color(white)(x)V_(color(red)"cone")=1/3pir^2hlarrcolor(blue)"volume of cone"
• " circumference (C)"=2pir
V_(color(red)"cone")=1/3pir^2xx18=6pir^2
"now volume is given as "1014pi
rArr6pir^2=1014pi
"divide both sides by "6pi
(cancel(6pi) r^2)/cancel(6pi)=(1014cancel(pi))/(6cancel(pi)
rArrr^2=1014/6=169
rArrr=sqrt169=13
rArrC=2pixx13=26pilarrcolor(red)"exact value"
The volume of a cone is
Explanation:
So, in your case:
The
Multiply both sides by 3
Then divide both sides by 18
Then, take the square root of both sides
Since this is a distance , use the positive square root since distances can't be negative, so r = 13.
Then, the circumference of a circle is
So,
That is your answer and is an exact value since it is in terms of