Find the radius of a cone with a height of 3m and a volume of 30m cubed.
So far I have 90m cubed / 3m = pi(r^)3m/3m.
Then I get stuck. Help! I'm really bad at math. ):
v = 1/3 pi r^2 h
so,
pi/3 r^2 (3) = 30
r^2 = 30/pi
r = ...
No worries! Let's break down the problem step by step to find the radius of the cone.
First, let's recall the formula for the volume of a cone:
Volume of a cone = (1/3) * π * r^2 * h,
where π is a constant (pi), r is the radius, and h is the height.
You already have the volume of the cone given as 30m cubed, and the height as 3m. So we can rewrite the equation as:
30 = (1/3) * π * r^2 * 3.
Now, let's simplify the equation. To get rid of the fraction, we can multiply both sides of the equation by 3:
30 * 3 = π * r^2 * 3.
This simplifies to:
90 = π * r^2 * 3.
Now, divide both sides of the equation by (π * 3) to isolate r^2:
90 / (π * 3) = r^2.
To find the radius, we need to take the square root of both sides of the equation:
sqrt(90 / (π * 3)) = r.
Now, just plug this equation into a calculator to get the numerical value of r. Remember to use the value of π as approximately 3.14159 or simply use the π symbol on your calculator.
I hope this explanation helps you solve the problem!