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

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: (1) What is the approximate volume of a thin cylindrical shell with height 2, radius 3, and…

A: Solution ) Volume of the cylinder    V = πx2h        x = radius         Differentiate with respect…

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: A right-circular cone is to be circumscribed about a sphere of given radius. Find the ratio of the…

A: Let R be the radius of the cone, l its slant height and h be the height. V= 13πR2h We have to make…

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

A:

Q: Derive the formula for the volume of a sphere of radius r by slicing.

A: We have, a sphere of radius r. The differential element shown in the figure is cylindrical with…

Q: 1. Find the exact lateral area, surface area and volume of a right cone with a radius of 9 cm and a…

A:

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: Calculate the volume generated by the circle x^2 + y^2 -4x=-3 that revolves around ox

A:

Q: Find the volume of the solid whose base is an isosceles triangle (with base 6 meters and sides 5…

A: Given a solid whose base is an isosceles triangle (with base 6 meters and sides 5 meters) and whose…

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

A:

Q: Find the total surface area of a frustum of a cone having radius of the upper base of 2 cm, radius…

A:

Q: 5. Find the volume common to two circular cylinders, each of radius r, that intersect at right…

A:

Q: 15. Let the cap of height h in a sphere of radius r have volume V.

A: In this question we will use basic of calculus i.e application of integration. We will assume a…

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

A:

Q: 10. Find, among all right circular cylinders of fixed volume V, the one with smallest surface area…

A:

Q: Consider a right-circular cylinder of diameter 1. Form a wedge by making one slice parallel to the…

A: The diameter of the right circular cylinder is d=1. The angle which is made by other slide to the…

Q: 6) Find the volume of a cylinder with lateral area 112n and radius 7.

A:

Q: Compute the volume lying inside the sphere x2 + y? + z2 = 35 but outside of x² + y? = 19.

A:

Q: The line segment from (0,0) to (5,20) is revolved about the x-axis to form a cone. What is the…

A: First find equation of line then Use formula of volume

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

A:

Q: 22. What is the exact volume of a cone whose base radius is 9 feet and whose height is 13 feet? Show…

A: The volume of a cone = (1/3) πr2h cubic units Where, ‘r’ is the base radius of the cone ‘h’ is the…

Q: 5. A 210° sector is cut out of a circular piece of tin with radius 6 in and bent to form the lateral…

A:

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: 4. Find the radius of the right circular cone with least volume that can be circumscribed about the…

A: Formula Used: Volume of Cone = 13πR2h where R,h denote the radius and height of right circular…

Q: A right circular cone has a slant height of 12 ft and a lateral area of 96™ ft². Find its volume.

A: Let r be the length of radius of base, h be the altitude of the circular coneand l be the length of…

Q: Find the height of a right circular cylinder of maximum volume, which can be inscribe in a sphere od…

A: Topic:- geometry

Q: Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 3.

A: Cone: The volume of right circular cone V=13πr2h Where r is the radius of the circular base of the…

Q: 23. Calculate the volume of (Figure 26). a cylinder inclined at an angle 0 = 30° with height 10 and…

A:

Q: A cone has radius 8 and height 6. Find the volume.

A: Given: A cone has radius 8 and height 6. To determine: Volume of the given cone.

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: What is the total surface area of a right circular cone of height 14 cm and base radius 2 cm?

A:

Q: Find the volume cut from the sphere radius r = 15 by the cone ki+

A: To compute the volume using spherical coordinates, use the following formula. V=∭r2sinθdrdθdϕ

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: 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: 9. Find the demensions of the right circular cylinder of largest volume that can be inscribed in a…

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Q: 2. Find the largest volume of a cylinder that fits into a cone has base radium R and height

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Q: Show that the surface area of a closed cuboid with square base and given volume is minimum , when it…

A:

Q: A right circular cone of radius 3 cm has a curved surface area of 47.1 cm2  Find the volume of the…

A:

Q: A sphere with radius r is inscribed in a cylinder. Find the volumeof the cylinder in terms of r.

A: let a right circular cylinder of radius 'R' and height 'H' is inscribed in the sphere of the given…

Q: What is the difference in volume between a sphere with radius rr and a sphere with radius 0.3r0.3r?

A: Given query is to find the difference in the volume.

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

A:

Q: Find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius…

A:

Q: A right prism has height x and bases that are equilateral triangles with sides x. Show that the…

A: Given, A right prism has height x and bases that are equilateral triangles with sides x.

Q: What is the volume of the torus whose region is inside the circle

A: (x-3)2 + y2 = 1. Take it as the form (x-b)2 + y2 = a2, where b=3 and a=1.

Q: d the volume of losed by y = line

A: Here the function is f(x)=x , y=0 and x=9  is revolved about the line x=9

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…

Q: 2.The monument of Cestius in Rome which is a square pyramid is a square pyramid 121.5 ft high with a…

A: According to question, Height of pyramid h = 121.5 ft, Base edge of square pyramid b = 98.4 ft

Q: Show that the surface area of a closed cuboid with square base and given volume is minimum, when it…

A: Let the length be x , breadth be x and height be y of a closed cuboid with a square base.So Volume…

Q: 4. A cone just fits inside a cylinder with a diameter of 8 m and a height of 11 m. What is the…

A: These are geometry based problem where volume of the cone and the volume of the empty space when a…