A coffee maker has a cone-shaped container to hold the coffee grounds. The radius of the container is 3 inches and the height is 7 inches. What is the volume, in cubic inches, of coffee grounds the container can hold? Round your answer to the nearest hundredth and use 3.14 for π
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The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height.
Plugging in the values, we get V = (1/3)(3.14)(3^2)(7)
V = (1/3)(3.14)(9)(7)
V = (1/3)(3.14)(63)
V = (1/3)(197.82)
V ≈ 65.94 cubic inches
To find the volume of a cone, we can use the formula V = (1/3)πr^2h, where r is the radius and h is the height.
First, let's find the radius of the cone by dividing the diameter by 2:
radius = 12 feet / 2 = 6 feet
Now we can substitute the values into the formula:
V = (1/3)(3.14)(6^2)(15)
V = (1/3)(3.14)(36)(15)
V = (1/3)(3.14)(540)
V = (1/3)(1695.6)
V ≈ 565.2 cubic feet
Therefore, the tank can hold approximately 565.2 cubic feet of water.
A water tank in the shape of a cone has a diameter of 12 feet and a height of 15 feet. What volume of water, in cubic feet, can the tank hold? Round your answer to the nearest tenth and use 3.14 for π
To find the volume of the cone-shaped container, we can use the formula for the volume of a cone, which is given by:
V = (1/3) * π * r^2 * h,
where V represents the volume, π represents the mathematical constant pi (approximately 3.14), r represents the radius, and h represents the height.
In this case, the radius is given as 3 inches and the height is given as 7 inches. Plugging these values into the formula, we get:
V = (1/3) * 3.14 * 3^2 * 7.
First, let's calculate 3^2, which equals 9. Then, let's multiply that by 7, which equals 63. Finally, let's multiply that by (1/3) and 3.14:
V = (1/3) * 3.14 * 9 * 7 = 197.22.
Therefore, the volume of coffee grounds the container can hold is approximately 197.22 cubic inches.