a stone is thrown into a cylindrical water tank 2 feet in diameter, causing it to rise 1.5 inches. what is the volume of the stone?
Does the tank or the water rise? Your question doesn't make that clear.
the water rises
the change in the volume of the water in the tank equals the volume of the stone
so volume change = Pi(r^2)h, where r is the radius and h is the height
so V = Pi(24^2)(1.5) cu inches
= appr. 2714 cu inches.
24 inches isn't that the diameter
To calculate the volume of the stone, we can use the concept of displacement of water. The rise in the water level by 1.5 inches is due to the displacement of water by the stone. Let's break down the steps to find the volume:
1. Determine the change in the water level: The water level rises by 1.5 inches.
2. Calculate the cross-sectional area of the cylindrical water tank: The diameter of the tank is 2 feet, so the radius is 1 foot (1/2 of the diameter). The cross-sectional area is given by the formula A = πr^2, where π is a constant (approximately 3.14159). Plugging in the radius, we get A = 3.14159 * (1^2) = 3.14159 square feet.
3. Convert the change in water level to the same units as the cross-sectional area: Convert the rise in water level from inches to feet. Since there are 12 inches in a foot, divide 1.5 inches by 12 to get 0.125 feet.
4. Calculate the volume of the stone: The volume of the stone is obtained by multiplying the change in water level by the cross-sectional area. Multiplying 0.125 feet by 3.14159 square feet, we get approximately 0.3927 cubic feet.
Therefore, the volume of the stone is approximately 0.3927 cubic feet.