Solve the problem. Use 3.14 for ð. Round to the nearest tenth, if necessary. A cylindrical container has a diameter of 10 in. and a volume of 549.5 in3. What is the height of the container?
To solve this problem, we need to use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given that the diameter of the container is 10 inches, we can find the radius by dividing the diameter by 2:
Radius = diameter / 2 = 10 in / 2 = 5 in
Now, we can substitute the known values into the formula:
549.5 in^3 = 3.14 * (5 in)^2 * h
Simplifying further:
549.5 in^3 = 3.14 * 25 in^2 * h
Divide both sides by (3.14 * 25 in^2) to isolate h:
h = 549.5 in^3 / (3.14 * 25 in^2)
Performing the calculation, we get:
h = 549.5 in^3 / 78.5 in^2
Rounding to the nearest tenth, we find:
h ≈ 6.99 inches
Therefore, the height of the container is approximately 6.99 inches.
The volume V of a cylinder is πr²h, where r=radius, h=height.
With diameter of 10", the radius is 5".
Thus
V=549.5=π(5)²h
and solving for h:
h=549.5/(π(5)²)=7"