THE VOLUME OF AN OBLIQUE CONE WITH EQUAL DIAMETER AND HEIGHT IS 18*3.14CM^3. FIND THE HEIGHT AND RADIUS (TO THE NEAREST CM).
PLEASE HELP THIS IS MY LAST TEST AND I GRADUATE!!! THANKS SO MUCH!!
the volume of a cone , regular or oblique,
= (1/3)πr^2 h
if h = 2r
V = (1/3) π r^2 (2r) = (2/3)π r^3
but (2/3)π r^3 = 18π , (I assumed your 3.14 was supposed to be π )
(2/3) r^3 = 18
2r^3 = 48
r^3 = 24
r = 24^(1/3) = appr 2.885 cm
or 3 cm to the nearest cm
neat little applet here for an oblique cone
http://www.mathopenref.com/coneoblique.html
To find the height and radius of an oblique cone with equal diameter and height, given the volume, we can use the formula for the volume of a cone.
The formula for the volume of a cone is given by:
V = (1/3) * π * r^2 * h
where V is the volume, π (pi) is approximately equal to 3.14, r is the radius, and h is the height.
We are given that the volume V is 18 * 3.14 cm^3. So we can write the equation as:
18 * 3.14 = (1/3) * π * r^2 * h
Simplifying the equation, we get:
r^2 * h = (18 * 3.14 * 3) / π
To find the height and radius individually, we need one more equation. We know that the oblique cone has equal diameter and height, which means r = h.
Substituting r = h, we get:
r^2 * r = (18 * 3.14 * 3) / π
Simplifying further, we have:
r^3 = (18 * 3.14 * 3) / π
To find the value of r, we need to evaluate the right side of the equation. Let's calculate it:
Value = (18 * 3.14 * 3) / π
Value ≈ 169.56 cm^3 (calculating the value)
To find the cube root of 169.56, we can use a calculator or estimate the answer.
Using a calculator, the cube root of 169.56 is approximately 5.2603.
So, the value of r (radius) is approximately 5.2603 cm.
Since the oblique cone has equal diameter and height, the height is also approximately 5.2603 cm.
Therefore, to the nearest cm, the height and radius of the oblique cone are both 5 cm.