10. The base of the solid is the disk x? + y? < 1. The cross-sections by planes perpendicular to the y-axis between y = -1 and y = 1 are isosceles right triangles with one leg in the disk. 0. x² + y? = 1

Q: 13. The volume generated when the region bounded by the curve x = /1+ y, the y-axis and the lines y…

A: Please rate

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: 25. Find the volume of the solid that is enclosed by the cone z = Vx² + y? and the sphere 22 + y? +…

A:

Q: The circular cross-section of the cylinder, y + z? = 4, can be obtained by cutting it along any…

A:

Q: 5. y=x³, x = 0, y = 8; about X = 2

A: The region is

Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

A:

Q: 2. The solid outside the cylinder x² + y² = 1 that is bounded above by the sphere x² + y? + x? = 8…

A: The solution is given below

Q: The area A(E) of the surface E that is the part of the surface z = xy that lies within the cylinder…

A:

Q: V=$t re h for r (geometry, volume of a spherical tuumor).

A:

Q: Reduce the surface integral ( S A.ds) of a cube of sides parallel to the three perpendicular axes,…

A: Here we can use divergence theorem to reduce the given surface integral. Divergence theorem states…

Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: Which bowl holds more water if it is filled to a depth of four units? • The paraboloid z =x? + y?…

A:

Q: e of the solid E whose boundaries are given in rectangular located inside the circular cone x? + y?…

A: In this question we will use basic of calculus i.e volume of cone. We will simply draw the given…

Q: 1. The hy per bola x²-y² = a² revolves about its transverse axis. Find the volume of a segment of…

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Q: 24 22. Find the volume generated by revolving about Ox the area bounded by the Ans. ra³. hyperbola…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

A:

Q: 1. Find the volume of the solid in the first octant bounded above by the sphere a? + y? + (z – 5)² =…

A:

Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: 6. What is the volume of the region which lies between the spheres p = 3 and p= 2 cos o, and inside…

A: we have to find the volume of the region which lies between the sphere ρ=3 &amp; ρ = 2cosϕ and…

Q: 13. The region bounded by y = x°, y = 0, and x = 2 is revolved about the line x= 2. Find the volume…

A: Formula: The volume of the solid revolution generated by using disk method is given by,…

Q: Find the olume of the solid cut Prom the sphere 8=2C@SQ by the Cone Z= Jx+ ý Ans/ T

A: The given question is related with triple integral. We have to find the volume of the solid cut from…

Q: What is the volume of the region which lies between the spheres p = 3 and p= 2 cos o, and inside the…

A: Volume is a 3-dimensional quantity which describes the amount of space available in solid. Volume of…

Q: 3. Find the volume of a solid enclosed by the parabolic cylinder y = x², the planes z = 0 and y +z =…

A:

Q: 4. For r > 0 and h > 0, show that the conical set S = (x, y, z) | x > 0, y > 0, z > 0, z2 h?(r2 - x²…

A: Given that the surface S is S=x,y,z|x&gt;0,y&gt;0,z&gt;0, h2=h2r2-x2-y2 We have to find the surface…

Q: 7. Find the volume and centroid generated by revolving the given plane area about y^2=4x, x=4; about…

A: Given that - y2 = 4x, x = 4; about x = 4

Q: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

A:

Q: 1. Consider the surface which is the part of the sphere r? + y? + 2? = 4 that lies above the cone z…

A:

Q: Consider the solid bounded by 4x² +y² +z? =9, and z> 4x? + y? with a Problem 8 constant density of…

A:

Q: Evaluate dV, where E lies between the spheres x2 + y? + z2 = 4 and x? + y? + z² E x² + y? + z? = 36…

A: x​=ρcosθsinϕ y=ρsinθsinϕ z=ρcosϕ ρ2 = x2+y2+z2 ​

Q: 4. Find the volume of the solid that lies within both the cylinder a²+y² = 1 and the sphere a2+y² +…

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Q: 5. Find the volume under the paraboloid = -a? – y?, and above the cone z = - p² + y?.

A:

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes h units apart.…

A:

Q: 2. Use a spherical coordinate system (p, 4, 0) to find the volume between (Зx2 + Зу?. the sphere x?…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: Find the volume of the largest box of the type shown in the figure, with one corner at the origin…

A: The volume of the box with one point at origin and another point at x,y,z is given by V=xyz. We want…

Q: : The area of the surface obtained by rotating the curve y = 2 In a, for 1 < a <e, about the a-axis,…

A: We have to find the integral that given the surface area.

Q: 4) By Diskuethod Detremin the volup Hiw Dx=1 and lnes y=1 aboat x=0 2) fex) = x? and line y:1 in the…

A: Given

Q: Compute the volume of the solid above the cone o = , and between the spheres p = 1 and p = 3. Hint:…

A: We have to use spherical co ordinate system

Q: ind the volume of the solid generated by revolving the region bounded by the graphs of the equations…

A: please refer to the image below.

Q: Find the volume trapped between the cone z = 2 – Vx² + y² (upper) and the paraboloid z = x² +y².…

A: We need to find volume.

Q: 4/ Calculus

A: Region is bounded by co ordinate planes, the plane and the surface.

Q: If the region bounder by the two curves is revolved about x = 4, what is the volume of the resulting…

A:

Q: 47. Find the distance between the spheres x? + y² + z² = 4 and x? + y? + z? = 4x + 4y + 4z – 11.

A: The equation of the spheres are given:

Q: 9. Find the volume of the solid enclosed by the cone z = Vx? + y? and the plane z = 4.

A: we have to find the volume of the solid

Q: 11- Find the volume of the solid that lies within both the cylinder x2 + y? = 1and the sphere x2 +…

A: In cylindrical coordinates the volume is bounded by cylinder r = 1 and sphere x2+y2+z2=4 We know…

Q: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

A: For a function, z=f(x,y) the surface area is calculated using the formula below. S=∬D[fx]2+[fy]2+1dA

Q: Find the volume.

A:

Q: (b) Find the volume and the surface area of the truncated cone made by the rotation of the solid…

A: From the given graph: Now, from the graph given that:    r = 2 unit, R = 4 unit, and h = 3 unit.…

Q: Use the method of disks to rotate a circle of radius r around the x axis and prove that a sphere of…

A:

Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

A: