Frustum of a Cone

To solve this problem, we need to understand the concept of a frustum of a cone. A frustum of a cone is a shape that is obtained by cutting a smaller cone from a larger cone. The larger cone is called the "top cone," and the smaller cone is called the "bottom cone." The frustum of the cone is the region between the top and bottom cones.

Given Information:
- The upper radius of the frustum of the cone (top cone) = 1.5 m
- The lower radius of the frustum of the cone (bottom cone) = 1 m
- Height of the frustum of the cone = 2 m
- Water is flowing into the frustum at a rate of 100 liters per minute
- The water rises in the tank at a rate of 0.04916 cm/s

Calculating the Volume of the Frustum:
The volume of a frustum of a cone can be calculated using the formula:

V = (1/3) * π * h * (R^2 + r^2 + R*r)

where V is the volume of the frustum, h is the height of the frustum, R is the radius of the top cone, and r is the radius of the bottom cone.

In this case, the volume of the frustum can be calculated as:

V = (1/3) * π * 2 * (1.5^2 + 1.5*1 + 1^2)
= (1/3) * π * 2 * (2.25 + 1.5 + 1)
= (1/3) * π * 2 * 4.75
= (8/3) * π * 2.75
≈ 23.183 m^3

Calculating the Rate of Water Flow:
The rate of water flow can be calculated using the formula:

Rate of Flow = Volume / Time

In this case, the volume of water flowing into the frustum per minute is given as 100 liters. To convert liters to cubic meters, we divide by 1000:

Volume = 100 liters / 1000
= 0.1 m^3

Therefore, the rate of water flow is:

Rate of Flow = 0.1 m^3 / 1 minute
= 0.1 m^3/minute

Calculating the Depth of Water:
To calculate the depth of the water, we need to determine how much the water level rises in a given time. We know that the water rises at a rate of 0.04916 cm/s.

To find the depth of the water, we can use the formula:

Depth = Rate of Rise * Time

In this case, the rate of rise is given as 0.04916 cm/s. To convert cm to meters, we divide by 100:

Rate of Rise = 0.04916 cm/s / 100
= 0.0004916 m/s

Let's assume the time taken for the water level to rise is t seconds.

Depth = 0.0004916 m/s * t seconds

Now, we know that the rate of water flow is 0.1 m^3