16. A frustum of a right circular cone with height h, lower base radius R, and top radius r. Find the volume of the frustum. (h = 6, R= 5, r = 2) R

Q: The base of a pyramid is a regular hexagon with sides y cmlong. The lateral edges are 2y cm long.…

A: The base area of the pyramid is the area of a regular hexagon with a side length of y cm.  So the…

Q: 17) If a right circular cone has a circular base with a diameter of length 10 cm and a volume of 50…

A: The diameter of circular base of the right circular cone is 10 m and so radius of circular base of…

Q: 2. Consider the first quadrant region bounded by y² = x, the x-axis and x = 4. Find the volume when…

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

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Q: Find the volume of a cap of a sphere with radius 50 and height h = 3.

A: volume of sherical cap with radius given r=50 and height=3

Q: 9. Find the volume of the solid whose base is the region enclosed by y = 2 –- x² and the x-axis and…

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Q: 3. Use cylindrical shells to find the volume of the solid eenerated when the shaded region is…

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Q: A torus is formed by revolving the region bounded by the circle x2 + y2 = 1 about the line x = 2 .…

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Q: A solid has a circular base of radius 3. What is the volume of the solid if vertical cross-sections…

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Q: Find the volume of the described solid S A frustum of a right circular cone with height  h ,…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x? = 8y,…

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Q: Calculate the volume of a cylinder inclined at an angle θ = 30◦ with height 10 and base of radius 4…

A: Given,  A cylinder with height 10 and base of radius 4. Also, it inclined at an angle of θ=30°.…

Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle…

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Q: 3. Determine the dimensions of the right circular cylinder, with the greatest volume, that can be…

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Q: Find the volume of the torus generated by revolving the circle (x−5)2+y2=4 about the​ y-axis. What…

A: Here, equation of circle is: (x-5)2+y2=4 So, the centre of the circle is (5,0) and radius will be 2.…

Q: If the region enclosed by the y-axis, the line y=2 and the curve y=sqrtx is revolved about the…

A: Proceed as shown below...

Q: Compute the volume lying inside the sphere x2 + y? + z2 = 46 but outside of x² + y? = 21.

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Q: A solid has a circular base of radius 3. What is the volume of the solid if vertical cross-sections…

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Q: Given the region bounded by y=×^3 ,X = 2, and the x-axis (in Quadrant I) is rotated about the line y…

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Q: 5. Find the volume of spherical wedge formed by rotating through an angle of 45 a semi circle of…

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Q: 3. If the region bounded by the curves y =x, y=0, and x =9 is the base of a solid, and cross…

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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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Q: Determine the surface area formed by revolving the shaded area 360∘ about the z axis.

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Q: A hole of radius r is bored through the center of a sphere of radius R. Find the volume V of the…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

A: I am attaching image so that you understand each and every step.

Q: Derive the formula for the volume of a sphere by revolving about the x-axis, the region bounded by…

A: We have to derive the formula for the volume of a sphere by revolving about the x-axis, he region…

Q: A hole is drilled through the center of a metal sphere of radius 6cm. The hole has a radius of 3cm.…

A: Volume of metal ring = 798.63 cm³

Q: 6. A solid has a circular base of radius 3. What is the volume of the solid if vertical…

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Q: 2. A right cylinder is inscribed in a cone with height 3 cm and radius of 9 cm. Find the largest…

A: We have to find the largest volume.

Q: A closed cylindrical container of total surface area 660cm^2 has radius 7cm.Find the volume (π=3.14)

A: We need to find the volume.  First we will find the height of cylinder.

Q: 9. Find the volume of a frustum of a right circular cone with height h, lower base radius R, and top…

A: Volume of frustom of right circular cone is given by

Q: Find the volume of a cap of a sphere with radius r=65 and height h=47.

A: Given,           The volume of a cap of a sphere with radius r=65 and height h=47.We know that,…

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x2 = 8y,…

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Q: 3. Find the volume of the region R when it is rotated around the y-axis. Show that this volume is…

A: When considering the cylindrical shell method, a thin cylinder is considered. The surface area of…

Q: 1. Use cylindrical shells to find the volume of the solid generated when the shaded region is…

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

Q: 5. The EXACT surface area of a right cylinder is 7807 in². If the radius is 10 in, find the height,…

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Q: Find the volume of the sdid of revolution below. (1,1) 05 y=x

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Q: 3. The area on the second and third quadrant of the circle x^2+y^2=36 is revolved about the line…

A: Sketch the region and find limit in y variable.

Q: Find the volume of the first octant region bounded by the coordinate planes and the parabolic…

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Q: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

A: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

Q: If the lateral area of a right circular cylinder is 88 and its volume is 220, find the radius. А. 2…

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Q: A right prism has height h and bases that are regular hexagons with sides s. Show that the volume is…

A: It is given that bases are regular hexagons with sides 's'. It clear from the figure that a hexagon…

Q: 2 Find the volume of the salid in the by the Coordinates planes, the plane x=3 , and the parabolic…

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Q: 19. Find the volume obtained by rotating f(r) = x(1 – x) around the x-axis. Then find the volume…

A: The given curve is yx=x1-x.To find:aThe volume of solid obtained by rotating about x-axis.bThe…

Q: 3. Find the volume of the region common to the interiors of cylinders a? + y² = 1 and r? + z2 = 1

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Q: 4) The base of a solid is the region between the curve, y (9+ x) = x' (27 – x), 0<x<27, y20 and the…

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Q: = 36 is revolved about the line The area enclosed by the curve 4x² + 9y? = 2. Find the volume…

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Q: Find the volume of the three-dimensional body caused by rotating a given straight line around an…

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Q: 1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of…

A: There are two Theorem by Pappus 1st for surface area of revolution and 2nd for volume of revolution…