A tank in the shape of an inverted right circular cone has height 5 meters and radius 3 meters. It is filled with 2 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is δ=1080kgm3.

Q: An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work (in J) needed to pump…

A: The aquarium is  long,  wide and  deep.We have to  calculate the work needed to pump half of the…

Q: A hemispherical tank of radius 6 feet is positioned as in the figure below. How much work is…

A:

Q: A right cylindrical can has a radius and height of 50 and 120 cm, respectively. Find the approximate…

A: Let  r  and h be the radius and height of the cylinder .Then the volume of the cylinder  V(r,h) =…

Q: A tank in the shape of an inverted right circular cone has height 4 meters and radius 3 meters. It…

A:

Q: The lateral area of the right circular cylindrical water tank is 92 sq m and its volume is 360 cubic…

A: Let's find.

Q: A trough is 5 meters long, 2.5 meters wide, and 2 meters deep. The vertical cross-section of the…

A: Given that the trough is L=5m long, W=2.5 wide, and 2 m deep. The trough is full of water. We need…

Q: A rectangular pontoon is 7 m long and 3 m wide. The welghl pontoon is 30 tons. Determine the…

A:

Q: A farmer wants to repaint a thin, cylindrical water tank on their property. He only needs to paint…

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Q: Approximate graphically the radius and height of a cylindrical container with volume 80cubic inches…

A: Given, Volume, V=80 cubic inchesLateral surface area, A=55 square inches The formula for the volume…

Q: A horizontal cylindrical tank 4 ft in diameter and 10 ft long is full of water. Find the work done…

A: A horizontal cylindrical tank has a diameter 4 ft and a height 10 ft Therefore, the radius of the…

Q: Find volume if area enclosed is rotated about y= -2.

A: To find the volume if the area enclosed by the below curves is rotated about y = -2.

Q: A tank in the form of an inverted right-circular cone is 8m across the top and 10m deep. The tank is…

A: Given: Diameter = 8m Radius, R = 4m Height of tank, H = 10m Height upto which tank is filled, h = 8m…

Q: A full water tank in the shape of an inverted right circular cone is 8 m across the top and 4 m…

A: Draw the figure according o given information, which is given below. Here, diameter D= 8 m Hence,…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.