Find the volume of the figure. the figure is in the website below. For calculations involving π, give both the exact value and an approximation to the nearest hundredth of a unit. Let d = 8 and h = 18.
www.webassign.net/aufexc3/7-4-002-alt.gif
To find the volume of the figure, we need to determine the shape first. From the given website, it appears to be a cone with radius "d" and height "h".
The formula for finding the volume of a cone is V = (1/3) * π * r^2 * h, where "r" is the radius and "h" is the height.
Given that the radius (diameter/2) is 8 units and the height is 18 units, we can substitute these values into the formula:
V = (1/3) * π * (8/2)^2 * 18
Simplifying:
V = (1/3) * π * 4^2 * 18
V = (1/3) * π * 16 * 18
V = (1/3) * π * 288
V ≈ 301.59 cubic units (rounded to the nearest hundredth)
To find the volume of the figure in the given website, you can identify it as a cone. The formula to calculate the volume of a cone is V = (1/3)πr^2h, where "r" is the radius of the base and "h" is the height of the cone.
First, let's determine the radius "r" of the cone. In the given figure, the diameter of the base is given as "d = 8". Since the radius is half of the diameter, we can calculate the radius as r = d/2 = 8/2 = 4.
Next, we'll substitute the known values into the formula and calculate the volume. Using the given height "h = 18" and radius "r = 4", the formula becomes: V = (1/3)π(4^2)(18).
Now, let's calculate the exact value of the volume using the exact value of π. π is approximately 3.14159.
V = (1/3)π(4^2)(18)
= (1/3)π(16)(18)
= (1/3)(3.14159)(16)(18)
≈ 301.59288 cubic units
To obtain an approximation of this value to the nearest hundredths place, we will round it:
V ≈ 301.59 cubic units.
Therefore, the volume of the given figure is approximately 301.59 cubic units.
volume of a cone = (1/3)π*r^2*h
You are given d = 8, so r = 4
Fill in your values and evaluate.