(b) A cake is shaped like a hemisphere of radius 4 with base on the xy-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the xy- plane and separated by an angle of . 2 п 3 (bl) Use a double integral to find the volume of the slice for (b2) Now suppose that the cake is shaped like a cylinder with the same radius and you take a slice in the same way with the same angle. How high the cake should be so that you get the same amount of cake as in part (bl)?

Q: 12. The part of the cylinder x² + z² = 16 that lies between the planes x Find the area of the…

A: We know that if height of a cylinder be h Units and radius be r units then curved surface area of…

Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: Find the surface area of the region formed by the portion af the plane y+z= 10 inside the cylinder +…

A:

Q: Find the area of the portion of the sphere of radius 10 (centered at the origin) that is in the cone…

A:

Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: 5 (b). ( the base radius making the surface area minimum. ) Consider a cylinder having fixed volume.…

A: Given a cylinder having fixed volume.

Q: An open-top rectangular box is being constructed to hold a volume of 200 cm³ The base of the box is…

A:

Q: What is the area of the enclosed surface bounded by the x-axis, x = 2 and y=x2 ?

A: The area under the curve can be calculated by the integration. The formula for the integration is…

Q: Find the volume of the region under the surface z = 9x5 and above the triangle in the xy-plane with…

A:

Q: Find the area of ​​the plane x + y + z = 6 in cylinder X² + y² = 4

A: According to the given information, it is required to find the area of the plane in the cylinder.

Q: Q3/ The surfaces p = 3, p=5, p = 100, p = 130, z= 3, and z= 4.5 define a closed surface. Find (a)…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Find the surface area of the closed circular cylinder of greatest volume that can be inscribed in a…

A: solution:

Q: 3- a) Find the area of the region in the first quadrant between, y = IN and y = 1/4x² 2 b) Find the…

A:

Q: Find the surface area of the portion of the half ball with radius which cuts off by the cylinder x2…

A: Concept: The surface area of the half ball is given by: A=∬1+∂z∂y2+∂z∂x2dA Where ∂z∂y, ∂z∂x is the…

Q: Compute the volume of the column with a square base R= {(x,y): |x|< 3, |y| <3} cut by the plane z =…

A: We have to find volume whose base is square-

Q: Find the area of the shaded region under the quarter circle of radius 2 below. (hint: divide the…

A: Solved below

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Find the slope of the tangent to the curve x2+y2=25 at (3,4). 2x+2ydydx3,4=0dydx3,4=-xydydx3,4=-34

Q: The total amount of a cylinder inserted into a hemisphere of radius 1 unit Finds the maximum value…

A:

Q: Find the exact volume of the solid formed in the first octant bounded above by the cone z = 2-√√x² +…

A: We have to find the exact volume of the solid formed in the first octant bounded above by the cone…

Q: how/demostrate that the surface

A: