A water tower has a height of 25 meters and a width of 16 meters. What is the volume of the water tower?(1 point)
Responses
7,850 cubic meters
7,850 cubic meters
15,700 cubic meters
15,700 cubic meters
5,024 cubic meters
5,024 cubic meters
20,096 cubic meters
To determine the volume of the water tower, we would need to know its shape. A water tower can have various shapes, such as cylindrical, spherical, or a combination thereof. Commonly, water towers are cylindrical with a dome on top. However, with the information provided, we cannot definitively determine the shape of the water tower, and thus we cannot calculate its exact volume.
But let's make an assumption for the purpose of this question. If we assume the water tower is a perfect cylinder (which is a common shape for water towers), then we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given the width of the tower is 16 meters, the radius would be half the width, which is 8 meters. The height of the tower is given as 25 meters.
So, the volume of the cylindrical part of the water tower would be:
Volume = π * (8 meters)^2 * 25 meters
Volume = π * 64 meters^2 * 25 meters
Volume = π * 1600 meters^3
Volume = 3.14159 * 1600 meters^3
Volume = 5026.55 meters^3 (approximately)
Rounded to the nearest whole number, the volume would be approximately 5,027 cubic meters. However, this does not include any domed top that might exist, and the increments on the options do not seem to include this figure precisely. If we look at the provided options, the option closest to our calculated volume is:
5,024 cubic meters
Without more specific details about the shape of the water tower or any additional structures that may contribute to the total volume, we cannot provide a more precise answer. If the water tower includes a dome or other shapes, the total volume could be larger.
Describe the volume of the cylinder with a base radius of 2.5 in. and a height of 9 in.(1 point)
Responses
* π ( 9 )^2 ( 2.5 )^3in
* ( 2.5 ) ( 9 )^3in
* π ( 2.5 )^2 ( 9 )^3in
* π ( 2.5 ) ( 9 )^3in
The volume of a cylinder can be found using the formula:
Volume = π * radius^2 * height
For a base radius of 2.5 inches and a height of 9 inches, we plug these values into the formula:
Volume = π * (2.5 inches)^2 * 9 inches
So, the correct expression for the volume is:
π * (2.5 inches)^2 * 9 inches
None of the provided responses match this expression exactly. However, based on the standard formula for the volume of a cylinder, the correct response should be:
π * (2.5 inches)^2 * 9 inches
None of the given options match exactly, but the closest seems to be:
π ( 2.5 )^2 ( 9 )^3in
This response has an error in the exponent applied to the number 9; it should not be cubed. The correct volume expression does not have any exponents on the number 9, as the height should not be cubed in the formula for the volume of a cylinder. It appears to be a typographical error in the options provided. The correct volume formula once again is:
Volume = π * (2.5 inches)^2 * 9 inches
Find the volume of a cylinder with a height of 12 inches and a diameter of 8 inches.(1 point)
Responses
2,411.52 cubic inches
2,411.52 cubic inches
150.72 cubic inches
150.72 cubic inches
602.88 cubic inches
602.88 cubic inches
1,808.64 cubic inches
To find the volume of a cylinder, you use the formula:
Volume = π * radius^2 * height
Given that the height is 12 inches and the diameter is 8 inches, first find the radius by dividing the diameter by 2:
Radius = Diameter / 2
Radius = 8 inches / 2
Radius = 4 inches
Now plug the values into the volume formula:
Volume = π * (4 inches)^2 * 12 inches
Volume = π * 16 inches^2 * 12 inches
Volume = π * 192 inches^3
Volume = 3.14159 * 192 inches^3
Volume = 602.88 inches^3 (approximately)
So the volume of the cylinder is approximately 602.88 cubic inches. The correct response from the options provided is:
602.88 cubic inches