A quarry shaped like a cone has a height of 42 ft and a diameter of 47 ft.
What is the volume of the quarry?
Round your answer to one decimal place and use 3.14 to approximate pi.
ft3
v = 1/12 pi d^2 h
now plug and chug...
To find the volume of a quarry shaped like a cone, we can use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius of the base of the cone, and h is the height of the cone.
Since the diameter of the quarry is given as 47 ft, we can divide it by 2 to find the radius: r = 47 ft / 2 = 23.5 ft.
Now we can substitute the values into the formula:
V = (1/3) * 3.14 * (23.5 ft)^2 * 42 ft.
Calculating this expression:
V = (1/3) * 3.14 * (552.25 ft^2) * 42 ft.
Simplifying:
V ≈ 3.14 * 552.25 ft^2 * 14 ft.
V ≈ 3.14 * 7731.5 ft^3.
V ≈ 24272.01 ft^3.
Rounding to one decimal place:
V ≈ 24272.0 ft^3.
Therefore, the volume of the quarry is approximately 24272.0 ft^3.