A right circular cylinder is inscribed inside a sphere with radius r=3 inches. Find the maximum volume of the right circular cylinder. Volume of cylinder: V = Tr²h. 3 y O 127 in³ O 9T/3 in³ O 127/3 in³ O 9n in3

Q: Find the volume of the cap of a sphere of radius r and height h for h < r.

A: The equation of the sphere with radius r is x2+y2+z2=r2. Determine z2 from the equation of sphere.…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y? + z2 99 and the upper cone z? = 3x2 +…

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Q: Find the volume of the solid that lies under the sphere: x2 +y? +z? -2z=0 and above the cone: z=3(x²…

A: Solid lies under the sphere x2+y2+z2-2z=0⇒x2+y2+z-12=1 and above the cone z=3x2+y2 Now z=3x2+y2 and…

Q: Find the volume of the cylinder. Either enter an exact answer in terms of T or use 3.14 for T. 4…

A: To find The volume of the cylinder

Q: ® Eualuate the inteyral- ... taken. throughout the volume o f sphere b=2+

A: To evaluate ∫∫∫1a2-x2-y2-z2dx dy dz Taken throughout the volume of sphere x2+y2+z2=a2

Q: Find the volume of the solid above the cone z2= 3(x2 + y2 ), z ≥ 0 and below the sphere x2+ y2+ z2 =…

A: We convert the units in spherical coordinate. The cone is given as,  The sphere is given as, The…

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: Find the volume of the solid cut from the thick-walled cylinder 1 ≤ x2 + y2 ≤ 2 by the cones z =…

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Q: Find the volume of the solid that lies inside both the cylinder x² + y² = 16 and the sphere x² + y²…

A: Given cylinder and sphere x2+y2=16x2+y2+z2=36 clearly, Here we need to find volume inside both…

Q: Find the volume of liquid needed to fill a sphere of radius R to height h = R %3D 3

A: To find → volume of liquid needed to fill a sphere of radiusR to height h=R3

Q: Select the formula for the Volume of the cone 2. T:r·h+ 2·T• r2 1 T• p2 . h 3 O2. T. r2 . h T:r·h² +…

A: The volume of a cone of radius 'r' and vertical height 'h' is given by the formula     Volume of…

Q: Find (a) the volume and (b) the surface area of the sphere. Use 3.14 as an approximation for z. 52…

A: Volume= 43πr3 Surface area=4πr2

Q: Find the volume of the part of the ball p < a that lies between the cones o = T/6 and ¢ = T/3. = 10

A: Given ball ρ≤a lies between cones ϕ=π6 and ϕ=π3.

Q: Find the volume of the region cut from the solid sphere (x2 + y2 + z2 < 4a2) by the cylinder 40 (x²…

A: Given x2+y2+z2≤4a2x2+y2=a2

Q: b) Find the volume of an inverted cone defined by: i. R< 2 and 0 <0 <"/3

A: the given question is taken from the calculus in which we have to find the volume of the cone so…

Q: The volume of a right circular cone of radius a and height y is given by V : ' = ma²y. Suppose that…

A: From the given problem; The expression for the volume of the cone is: V=13πx2y And The volume of the…

Q: Find the volume of liquid needed to fill a sphere of radius R to height . R y

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Q: Q3-Find the volume common by the plane x+y=a? & x*+z=a? ?

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Q: Find the volume of the cone. Either enter an exact answer in terms of T or use 3.14 for T. units

A: Given,           Radius of cone (r) = 5 unit           Height of cone (h) = 6 unit           Volume…

Q: Find the volume of S above the cone where z V + y and inside the sphere where a+ y? + 2 <9.

A: Let S be the region above the cone z=x2+y2 and inside the sphere x2+y2+z2≤9.

Q: A body T with the parameters  (1/2)(sqrt(x^2)+(y^2))≤z≤sqrt(16-(x^2)-(y^2) Use the sphere…

A: The given problem is to find the volume of the body formed by the cone and spherical region, we have…

Q: Find the volume of the solid that lies within the cylinder x2 + y? = 4, above the (x, y)-plane, and…

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Q: Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by the…

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Q: The volume of the solid that results when the shaded region revolve around the indicated X-axis 4.…

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Q: Determine the diameter of a closed cylindrical tank having a volume of 11.3 m? to obtain a minimum…

A: Formula: Volume of cylinder: πr2h Surface are :2πrh +2πr2

Q: ind the mass of the lamina described by the inequalities, given that its density is p(x, y) = ху. 0<…

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Q: Determine the diameter of a closed cylindrical tank having a volume of 11.3 m to obtain a minimum…

A: The volume of the closed cylindrical tank is 11.3 m3

Q: Q5: A- Find the mass of the region cut from the sphere x+y+z=a² by the cone z = √x² + y² if the

A: We have to find the mass of the region cut from the sphere by cone.

Q: For the right circular cylinder, suppose that r = 5 in. and h = 6 in. Find the exact and approximate…

A: Given:               Right circular cylinder with radius(r)=5 inch;…

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Q: Let V be the volume of a pyramid of height 20 whose base is a square of side 6. 20 6 Use similar…

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Q: Find the volume of the cone. Either enter an exact answer in terms of T or use 3.14 for T. 5 units3

A:

Q: Find the volume of liquid needed to filla sphere of radius R to height R y V

A: Given that  Radius of sphere = R       and Find volume of liquid  at height at R/2.

Q: Let the radius of the cylinder be r cm and the height of the cylinder h cm.

A: Consider the labelled diagram below for the cone with the largest cylinder underneath.

Q: Find the volume of liquid needed to fill a sphere of radius R to height h = R.

A: answer is in next step. please give a like!!

Q: +v² , but outside Find the volume of the solid in the first octant under the upside-down cone :=6-…

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Q: The volume of a right circular cone of radius z and height y is given by V : 1 A2²y. Suppose that…

A: Given volume of  a right circular cone by expressionV=13πx2y       ......(1)And V=60π cm3

Q: 4.) Find x so that the volume of the U-shaped rectangular structure is equal to 165 cm3. 8 cm 10 cm…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Use the disk method to verify that the volume of a right circular cone is (1/3)π r2h, where r is the…

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Q: nd the radius of a sphere with volume z 113.04 in³.

A: Given that Volume of sphere = 113.04 in2

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: Find the volume of the cylinder. Either enter an exact answer in terms of T or use 3.14 for T. 2.

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Q: The volume of the solid generated by revolving the curve x = , about the y-axis between y = 0 and y…

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Q: Determine the solution in finding the dimensions of the right circular cylinder, with the greatest…

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Q: Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

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Q: Find the volume of liquid needed to fill a sphere of radius R to height R y V = 씨5

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Q: For a right circular cylinder, suppose that r= 6in and h= 7in Find the exact a) Lateral area L b)…

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Q: Q2) Find the volume of a cylinder with the dir below.* radius = 16 in; height = 27 in

A: Given for a cylinder radius = 16 inheight = 27 involume =?

Q: The solid shown consists of a right circular cylinder od diameter d and altitude of h, surmounted by…

A: The solid shown consists of a right circular cylinder od diameter d and altitude of h, surmounted by…

Q: Use the disk method to verify that the volume of a sphere is (4/3)π r3 , where r is the radius.

A: Volume of sphere of radius r is (4/3) πr3

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.