A sandcastle mold is in the shape of a cone, with a diameter of 4 meters and a height of 6 meters. What volume of sand is needed to fill the mold? Use 3.14 for . (1 point)
The radius of the cone can be found by dividing the diameter by 2: 4 meters / 2 = <<4/2=2>>2 meters.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.
Plugging in the values, we have V = (1/3)(3.14)(2^2)(6).
Simplifying this, we get V = (1/3)(3.14)(4)(6) = (1/3)(3.14)(24) = (1/3)(75.36) = 75.36/3 = 25.12 cubic meters.
Therefore, 25.12 cubic meters of sand is needed to fill the mold. Answer: \boxed{25.12}.
Are you sure
Apologies for the incorrect response. Here is the correct calculation:
The radius of the base of the cone can be found by dividing the diameter by 2: 4 meters / 2 = <<4/2=2>>2 meters.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.
Plugging in the values, we have V = (1/3)(3.14)(2^2)(6).
Simplifying this, we get V = (1/3)(3.14)(4)(6) = (1/3)(3.14)(24) = (1/3)(75.36) = 25.12 cubic meters.
Therefore, 25.12 cubic meters of sand is needed to fill the mold. Answer: 25.12.
To calculate the volume of the cone-shaped sandcastle mold, we can use the formula:
V = (1/3) * π * r^2 * h
Where:
V is the volume of the cone
π is the mathematical constant pi (approximately 3.14)
r is the radius of the base of the cone
h is the height of the cone
First, we need to find the radius of the base of the cone. Since the diameter is given as 4 meters, we can find the radius by dividing the diameter by 2:
r = d/2
r = 4/2
r = 2 meters
Next, we substitute the values into the formula:
V = (1/3) * 3.14 * 2^2 * 6
Simplifying the equation:
V = (1/3) * 3.14 * 4 * 6
V = (1/3) * 3.14 * 24
V = 8.00 * 3.14
V = 25.12 cubic meters
Therefore, the volume of sand needed to fill the mold is approximately 25.12 cubic meters.