Find the missing dimensions for each three-dimensional figure to the nearest tenth given the volume and other dimensions.
I'm not understanding the cones too much.
r=5in., v = 487in.3 How do I work it, given only the radius
you are missing the height, h
Volume of cone = (1/3)πr^2h
487 = (1/3)π(25)h
h = 487(3)/(25π) = appr. 18.6 in
To find the missing dimension in a three-dimensional figure, we can use the formula for the volume of the figure. In this case, we're dealing with a cone, so the formula is:
V = (1/3)πr²h
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
In your case, you're given the radius, r = 5 inches, and the volume, V = 487 cubic inches. You need to find the missing dimension, which is the height, h.
Let's rearrange the formula to solve for h:
V = (1/3)πr²h
Multiply both sides by 3 to get rid of the 1/3 fraction:
3V = πr²h
Divide both sides by (πr²) to isolate h:
h = (3V) / (πr²)
Now, you can substitute the given values into the formula to find the missing dimension:
h = (3 * 487) / (π * 5²)
Calculate the expression on the right side using the value of π as 3.14159:
h = (3 * 487) / (3.14159 * 25)
h ≈ 58.49 inches (rounded to the nearest tenth)
So, the missing dimension, the height of the cone, is approximately 58.49 inches.