the diameter of a cylinder is 3 yd. the height is 8 yd. find the volume of the cylinder in terms of pi and to the nearest tenth
To find the volume of a cylinder, you can use the formula:
V = πr^2h
where V represents the volume, π is a constant (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder.
In this case, we are given the diameter of the cylinder, which is 3 yards. The radius (r) can be found by dividing the diameter by 2:
r = 3 yd / 2 = 1.5 yd
Substituting the values into the formula, we have:
V = π(1.5 yd)^2 * 8 yd
Simplifying further:
V = π * 2.25 yd^2 * 8 yd
V = 18π yd^3
Rounding the final answer to the nearest tenth:
V ≈ 18 * 3.14159 yd^3 ≈ 56.5487 yd^3 ≈ 56.5 yd^3
To find the volume of a cylinder, we can use the formula: V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder's base, and h is the height of the cylinder.
Given that the diameter (d) of the cylinder is 3 yards, we can calculate the radius (r) by dividing the diameter by 2: r = d/2 = 3/2 = 1.5 yards.
The height (h) of the cylinder is given as 8 yards.
Now we have all the necessary values to calculate the volume (V):
V = πr^2h
= π(1.5^2)(8)
= π(2.25)(8)
= 18π cubic yards (as an exact value)
To find the volume to the nearest tenth, we can use the approximate value of π as 3.14159:
V ≈ 18 * 3.14159
≈ 56.54824
Therefore, the volume of the cylinder, in terms of pi and rounded to the nearest tenth, is approximately 56.5 cubic yards.
V = πr^2h
d = 2r
Insert values and solve.