An open tank has the shape of a right circular cone. The tank is 4 m across the top and 10 m high. How much work is done in emptying the tank by pumping the water over the top edge? The density of wate is 1000 kg/m.

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Q: for

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Q: A right circular cone has a slant height of 12 ft and a lateral area of 967 ft'. Find its volume.

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A: solution:-(1)outer radius, r=2 ftheight, h=6 ftouter surface area of cylinder= 2πrh+2πr2…

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A: We need to consider a section and then integrate accordingly.

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A: Solution:GivenBuilt around 2600 bceThe Great Pyramid of Giza in Egypt is 146 m.A square base of side…

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Q: A cone has a volume V. What base radius and height will minimize the lateral surface area?

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Q: A circular swimming pool has a diameter of 10 m, the sides are 4 m high, and the depth of the water…

A: According to the problem, we have

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Q: What is the pressure on a horizontal surface with an area of 2 m2 that is 4 m underwater?

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Q: Compute the volume lying inside the sphere x2 + y? + z2 = 35 but outside of x² + y? = 19.

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A: Given: Volume of cylindrical tank is 11.3m3.

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Q: Engr Thomas Pendot wants to construct a frustum from a right circular cone. At what distance from…

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Q: A horizontal cylindrical tank of length 15 m and diameter 2 m is half-full of water. How much work…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: Compute the volume lying inside the sphere x? + y? + z? = 37 but outside of x² + y? = 21.

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Q: The volume of the open cylindrical tank is

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.