(d) A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake. How much work is required to completely submerge the sphere? The density of the water is 1000 kg/m3. y=L-h y=0 L. h y=-h

Q: The density of a type of stone is 2000 kg/m^3. Find the work needed to build a stone cone with a…

A: Given: The density of the stone is 2000 kg/m3. The radius of the stone cone, r = 100m. And, the…

Q: 2. The linear density of a rod of length 4 m is given by p(x) = 9 + 2/ measured in kilograms per…

A:

Q: A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with a liquid of weight…

A: Note that the work done here can be given by: W=∫abρπr2h where ρ is the density, r is the radius and…

Q: A fluid has density 1000 kg/m³ and flows with velocity v = xi + yj + zk, where position is measured…

A: The density of the fluid is 1000 kg/m3. The flow velocity is xi+yj+zk, where position is measured in…

Q: A spherical tank with radius 4 m is half full of a liquid that has a density of 900 kg/m3. The tank…

A: Given data:     The given radius of the spherical tank is: r=4 m. The density of the liquid is:…

Q: A circular swimming pool has a diameter of 20 m, the sides are 3 m high, and the depth of the water…

A:

Q: volume solid= T1 da.dy.dz of 30 2पट 5 1. r.das.do.dz

A: Given, Volume of solid=∫∫∫v1·dx·dy·dz=∫03∫02π∫051·r·dr·dθ·dz

Q: A circular swimming pool has a diameter of 10 m, the sides are 3 m high, and the depth of the water…

A:

Q: a. A water tank has the shape of an upright cylinder with radius r = 1 meter and height 10 meters.…

A: Work needed = 37500 N m

Q: Built around 2600 bce, the Great Pyramid of Giza in Egypt (Figure) is 146 m high and has a square…

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

Q: A circular swimming pool has a diameter of 20 m, the sides are 4 m high, and the depth of the water…

A:

Q: The side of a cube increases at the rate of 5 m/sec. The rate at which the volume of the cube…

A: let side of cube is x then rate at which side increase is 5 m/secie.  dxdt=5 m/sec

Q: A circular swimming pool has a diameter of 12 m, the sides are 3 m high, and the depth of the water…

A:

Q: A circular swimming pool has a diameter of 20 m, the sides are 3 m high, and the depth of the water…

A: Consider the given information and find area of circle.

Q: A ring that weighs 80 grams is made of gold and silver. By measuring the displacement of the ring in…

A: Let ring contains x grams of gold. Density of gold = 19.3/cm3. So, the volume of gold ring =…

Q: 10. The linear density of a rod of length 1m is given by p(x) = 3/T – 2+1 in grams per centimeter,…

A: Here, the mass  m=∫01ρ(x) dx...(1)

Q: An aquarium 4 m long, 1 m wide and 3 m deep is full of water. Find the work needed to pump half of…

A: Workdone = integrate 0 to 0.5 F x dx.

Q: 3. Find the surface area of the object obtained by rotating y = 4 + 3x?, 1<x<2 about the y-axis.

A:

Q: A cylindrical tank, shown to the right, has height 8 m and radius 5 m. a. If the tank is full of…

A: Given :  (a).          height = 8 m            radius = 5 m           acceleration due to gravity, g…

Q: The Kinehc of a body with mass m energy 8 velo city 22K V IS k = mv? Show that %3D %3D Əvz

A: Topic-derivative

Q: A circular swimming pool has a diameter of 20 m, the sides are 3 m high, and the depth of the water…

A: this problem belongs to application of integration from calculus and we solve this using integration…

Q: A cube with sides 15 inches long is covered with a coat of fiberglass 0.2 inch thick. Use…

A:

Q: A circular swimming pool has a diameter of 14 m, the sides are 3 m high, and the depth of the water…

A: Given that the diameter of the swimming pool is 14 m. Hence, the radius of the pool is 7 m. The…

Q: Some European trucks run on energy stored in a rotating flywheel, with an electric motor getting the…

A: answer is in next step.

Q: A cylindrical reservoir of diameter 4 feet and height 6 feet is half full of water weighing 62.5…

A:

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: A storage tank is designed by rotating y = x² + 1; about the x- axis, y- axis, line x = 2, and…

A:

Q: The radius of a sphere decreases at a rate of 3 m/s. when the radius is 9 m, then the rate at which…

A:

Q: a closed cylindrical tank 10 ft in height and 4ft in diameter contains water with depth of 3ft and…

A: First, convert dimensions from feet to inches:Height of tank = 10 ft = 120 in,  Height of water = 3…

Q: A tank has the shape of an inverted right circular cone with height 11m and radius 19m. It is filled…

A:

Q: The side of a cube increases at the rate of 1 m/sec. The rate at which the volume of the cube…

A:

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A: Let the side of the cube be a m Then, given dadt=-7m/sec    (- sign indicates side is decreasing) To…

Q: Calculate the work (in joules) required to pump all water out of a full tank. Water exits here. d b…

A:

Q: A cylindrical tube of radius 2 cm and length 3 cm contains a gas. Since the tube is spinning around…

A:

Q: a very large cylindrical-shaped tank has a radius of 4 feet and a height of 15 feet. The tank is…

A: Given problem is : a very large cylindrical-shaped tank has a radius of 4 feet and a height of 15…

Q: LA circular swimming pool has a diameter of 14 m, the sides are 3 m high, and the depth of the water…

A:

Q: A circular swimming pool has a diameter of 16 m, the sides are 4 m high, and the depth of the water…

A:

Q: A milk container of height l6 cm is made of metal sheet in the form of frustum of a cone with radii…

A: Given data is : A milk container in the form of frustum. Height h=16 cm Lower radius r1=8 cmUpper…

Q: (b) Compute the work required to launch a 1000-kg satellite vertically to a height of 1000 km. You…

A:

Q: A circular swimming pool has a diameter of 16 m, the sides are 4 m high, and the depth of the water…

A:

Q: D. A Box with linear dimensions three times the box above... Surface Area = Volume = E. A Sphere…

A: The given cube has surface area 150 cm2 For part D: To find surface area and volume of box with…

Q: For a given cylindrical tank, the radius is 2m and the height is 18m. The tank is filled to a depth…

A:

Q: A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with a liquid of weight…

A: Solution

Q: A cylindrical tank, shown to the right, has height 7 m and radius 1 m. a. If the tank is full of…

A: Part a and b are solved

Q: Q1/ A cylindrical tank of length (L) has semicircular end sections of radius (R). the tank is placed…

A:

Q: An inverted conical tank with 14 m height and 6 m radius at the top is full of water. Calculate the…

A: A cone is a 3-D shape with a circular base and tapers smoothly over to an apex or a vertex. Three…

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,…

Q: A circular swimming pool has a diameter of 10 m, the sides are 3 m high, and the depth of the water…

A:

Q: The side of a cube increases at the rate of 10 m/sec. The rate at which the volume of the cube…

A:

Q: A circular swimming pool has a diameter of 10 m, the sides are 3 m high, and the depth of the water…

A: We have to solve this problem using integral calculus.

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.