Question

What is the volume of the water tank, to the nearest tenth of a cubic foot, if it is in the shape of a cylinder with the following dimensions: A) Radius = 3 feet, Height = 5 feet B) Radius = 4 feet, Height = 6 feet C) Radius = 2.5 feet, Height = 4 feet D) Radius = 7 feet, Height = 8 feet

Answer 1

A) The volume of the water tank, in the shape of a cylinder with a radius of 3 feet and a height of 5 feet, is approximately 141.4 cubic feet.

B) For a cylinder with a radius of 4 feet and a height of 6 feet, the volume of the water tank is approximately 301.6 cubic feet.

C) With a radius of 2.5 feet and a height of 4 feet, the volume of the water tank is approximately 78.5 cubic feet.

D) The water tank, characterized by a radius of 7 feet and a height of 8 feet, has an approximate volume of 1232.7 cubic feet.

Step-by-step explanation:

The formula for the volume (V) of a cylinder is given by
`\(V = \pi r^2 h\)`, where (r) is the radius and (h) is the height.

A) For the first scenario, where the radius is 3 feet and the height is 5 feet:

`\[V = \pi * (3^2) * 5 \approx 141.4 \, \text{cubic feet}\]`

B) In the second case, with a radius of 4 feet and a height of 6 feet:

`\[V = \pi * (4^2) * 6 \approx 301.6 \, \text{cubic feet}\]`

C) With a radius of 2.5 feet and a height of 4 feet:

`\[V = \pi * (2.5^2) * 4 \approx 78.5 \, \text{cubic feet}\]`

D) Lastly, for a radius of 7 feet and a height of 8 feet:

`\[V = \pi * (7^2) * 8 \approx 1232.7 \, \text{cubic feet}\]`

These calculations yield the volumes of the water tanks in each scenario, providing a comprehensive understanding of their capacities.