The volume of a tree stump can be modeled by considering it as a right cylinder. Shaniece measures its height as 1.5 ft and its radius as 36 in. Find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary.
First, we need to convert the radius from inches to feet:
36 inches = 36/12 feet = 3 feet
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Plugging in the values:
V = π(3)^2(1.5)
V = π(9)(1.5)
V = 4.5π cubic feet
Now, we need to convert the volume from cubic feet to cubic inches:
1 cubic foot = 12*12*12 = 1728 cubic inches
V = 4.5π * 1728
V ≈ 7731.3 cubic inches
Therefore, the volume of the tree stump is approximately 7731.3 cubic inches.
is this right?
I apologize for the mistake in my calculations. Let me correct it:
The volume of a cylinder is given by the formula V = πr^2h.
Given:
Height (h) = 1.5 ft
Radius (r) = 3 ft (converted from 36 inches to feet)
Now, we can calculate the volume of the stump:
V = π(3)^2(1.5)
V = π(9)(1.5)
V = 13.5π cubic feet
Next, convert the volume from cubic feet to cubic inches:
1 cubic foot = 12*12*12 = 1728 cubic inches
V = 13.5π * 1728
V ≈ 73756.43 cubic inches
Therefore, the correct volume of the tree stump is approximately 73756.43 cubic inches. Thank you for pointing out the error, and I appreciate your understanding.
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 22 feet and a height of 13 feet. Container B has a diameter of 20 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
After the pumping is complete, what is the volume of water in Container B, to the nearest tenth of a cubic foot?
To find the volume of water that was transferred from Container A to Container B, we need to calculate the volume of water in Container A and subtract it from the final volume in Container B.
Let's calculate the volumes of each container first.
Volume of Container A:
Radius of Container A = diameter/2 = 22/2 = 11 feet
Height of Container A = 13 feet
Volume of Container A = π(11)^2(13)
Volume of Container A = 5083.31 cubic feet
Volume of Container B:
Radius of Container B = diameter/2 = 20/2 = 10 feet
Height of Container B = 19 feet
Volume of Container B = π(10)^2(19)
Volume of Container B = 5990.52 cubic feet
Now, calculate the volume of water transferred from Container A to Container B:
Volume of water = Volume of Container A - Volume of Container B
Volume of water = 5083.31 - 5990.52
Volume of water ≈ -907.21 cubic feet
Since the volume cannot be negative, we take the absolute value to find the positive volume of water transferred:
Volume of water transferred = 907.21 cubic feet
Therefore, the volume of water in Container B after the transfer is approximately 907.2 cubic feet.
what is 907.21 to the nearest tenth of a cubic foot?
To round 907.21 to the nearest tenth of a cubic foot, we look at the digit in the hundredth's place, which is 2. Since this digit is less than 5, we do not need to round up.
Rounded to the nearest tenth, 907.21 is 907.2 cubic feet.