the diameter of a cylinder is 5 yd. the height is 8yd. find the volume of the cylinder in terms of pi and to the nearest tenth
The diameter of a cylinder is 3 yd. The height is 12 yd. Find the volume of the cylinder in terms of and to the nearest tenth.
To find the volume of a cylinder, we can use the formula:
Volume = π * r^2 * h
where r is the radius of the cylinder and h is its height.
Given that the diameter (d) of the cylinder is 5 yd, we can find the radius (r) using the formula:
r = d/2
So, the radius of the cylinder is 5/2 = 2.5 yd.
Now we can substitute the values into the volume formula:
Volume = π * (2.5)^2 * 8
Simplifying this equation:
Volume = π * 6.25 * 8
Volume ≈ 157.08 cubic yards (rounded to the nearest tenth).
Therefore, the volume of the cylinder is approximately 157.08 cubic yards.
To find the volume of a cylinder, we need to use the formula:
Volume = π * r^2 * h
Where:
- π is a mathematical constant that represents the ratio of a circle's circumference to its diameter, approximately 3.14159.
- r is the radius of the cylinder (half the diameter).
- h is the height of the cylinder.
In this case, the diameter of the cylinder is 5 yards, so the radius would be half of that:
Radius (r) = Diameter / 2 = 5 yd / 2 = 2.5 yd
The height of the cylinder is 8 yards.
Now, we can plug these values into the formula and calculate the volume:
Volume = π * (2.5 yd)^2 * 8 yd
Calculating this gives us:
Volume = 3.14159 * (2.5 yd)^2 * 8 yd
≈ 3.14159 * (6.25 yd^2) * 8 yd
≈ 3.14159 * 50 yd^3
≈ 157.0795 yd^3
Rounding to the nearest tenth, the volume of the cylinder is approximately 157.1 cubic yards.