A cone is mounted on one face and a hemisphere is mounted on the other face of a cylinder. All three shapes have the same radius. The height of the cone is the same as its radius and the height of the cylinder is thrice its radius. If the radius of the cylinder is 3.5 cm, what is the volume (in cm³) of the shape?

What is the height of a solid cylinder, whose radius is 5 cm and total surface area is 660 cm²?

A sector of 4% area is removed from a circular sheet of paper of radius 25 cm. If the remaining part is used to make a conical surface, then the ratio of radius and height of the cone is:

Find the volume of a toy of total height 108 cm made by joining a conical hat on a cylindrical bottle of radius 56 cm and the height of the cone is half of the height of the cylinder. (in cm³)

The total surface area of a hemisphere is equal to the total surface area of a sphere. What is the ratio of the volume of the sphere to that of the hemisphere?

The height of a cylinder is 5 cm more than its radius and the radius of a sphere is 7 cm. The total surface area of the sphere is 220 cm² less than that of the cylinder. What is the height of the cylinder? (in cm)

The diameter of a hemisphere is 42 cm. There is also a sphere whose radius is 2/3rd of the radius of the given hemisphere. What is the difference between the volume of the hemisphere and the sphere in question?

The ratio of volumes of a cone and cylinder is 8 : 81, and the height of the cone is 66.66 % of the height of the cylinder.  If 9 cones and 5 cylinders are melted to form 4 spheres of radius 3 cm each. Find the difference between the volume of the cone and the volume of the cylinder.

The height of a cone is 14 cm. If the volume of the cone is 2,112 cm³, then find the ratio of the height of the cone to the radius of the cone. {Take π = (22/7)}

The volume of a cylinder and a cone, of the same radius 'r', are equal. The height of the cylinder is given as 'H' and the height of the cone is h What will be the ratio of slant height of the cone to the height of the cylinder?

A wire of diameter 4 mm is bent in the form of a cylinder with a curved surface area of 1672 cm² and a height of 38 cm such that there are no open loops. Find the length of the wire and the number of loops formed by it.

Find the total surface area of a hollow hemisphere whose outer and inner radii are 5.6 cm and 1.4 cm respectively.

The radius of the cylinder is 7 cm and the curved surface area of the cylinder is equal to the total surface area of the cube, and the side of the cube is 14 cm. Find the height of the cylinder. (approx.)

A toy is prepared by a 12 cm high cone made above a base of a cylinder. The total height of the toy is 22 cm. If the radius of the base of a cylinder is 9 cm, then what is the volume of the whole toy?

A Solid cone is placed on top of a cylinder. If the radius of the Solid cylinder and cone is 5 cm and the height is 18 cm and the height of the entire solid is 30 cm. Then find the total surface area of the solid.

The volume of a cylinder is numerically equal to the surface area of a sphere. If the height of the cylinder is 16 cm then find the ratio of the plain surface area of the cylinder and the surface area of the sphere.

A sphere of radius 21 cm is melted to create 40 hollow cylinders of thickness 2 cm, outer radius 8cm, and height 10 cm. Find the volume of the cuboid made by the leftover.

A factory owner has a cylindrical-shaped metal sheet with a radius of 15 cm and a height of 70 cm. The sheet is melted and recast into small pieces of the cubical box. If the length of the side of the box is 5 cm, then find the total number of boxes so formed.

Some students made a robot. The face of the robot is circular in shape with a radius of 12.3 cm, and its middle part is cubic in shape with a length of 123.7 cm, width of 75.5 cm, and height of 12.3 cm, and it has two cylindrical legs with a radius 15.10 cm and height 10.5 cm. Find the volume of the robot. (round off to two decimal places)

A hollow spherical shell is made of a metal of density 9 g/cm3. Its internal and external radius are 10 cm and 13 cm, respectively. What is the weight (in kg) of the shell ?  (take \(\pi = \frac{22}{7}\))

The inner radius of an inner hemi-spherical vat is 21 cm. This vat is filled with the help of small cylindrical bottles. If the radius of the base of the bottle is 7/2 cm and the height by 12 cm, then how many bottles are required to fill it?

Ratio of the radius of cone to cylinder is 1 : 2 and the volume of the cylinder is 4928 cm³. If the height of the cylinder is 8 cm and the slant height of the cone is 24 cm, then find the volume of the cone.

A right circular solid cylinder has radius of base 11 cm and height is 28 cm. It is melted to form a cuboid such that the ratio of its side is 4 : 6 : 9. What is the total surface area (in cm²) of the cuboid?

A flower vase is in the form of a frustum of a cone. The perimeter of the ends are 88 cm and 16.8π cm. If the depth is 21 cm, find how much julep it can hold. (in cm³)

A hollow spherical shell is made of a metal with a density of 36 g/cm³. Its internal and external radius are 9 cm and 11 cm, respectively. What is the weight (in kg) of the shell ? ( take π =\(\frac{22}{7}\))

A clay cylinder of height 42 cm is converted into a cone of the same radius as that of the cylinder. If the volume of the cylinder is 52,800 cm³, then the radius (in cm) of the cone is:

(Use π = \(22 \over 7\))

A cylindrical pillar has a curved surface area of 264 m²  and a volume of 924 m³. What is the ratio of the diameter and height?

9 A cylindrical rod has an outer curved surface area of 1900 cm². If the length of the rod is 39 cm, then the outer radius (in cm) of the rod, correct to two place of decimal places, is: (Take π = \(22\over7\))

The circumference of the base of the cylindrical vessel is 154 cm and its height is 49 mm. How many litres of water can it hold? (correct to three places of decimals, use (\(\pi = \frac{22}{7}\))

An open water drum is in the form of a cylinder. The height of the drum is 79 m and its internal diameter is 78 m. Find the area (in m² , rounded off to one decimal place) that needs to be painted if one wants to paint the inside of the drum. Take π = \({22 \over 7}\)

A sector of radius 10.5 cm with the central angle 120° is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in cm³) of the cone so formed?

The radius of the base and height of a solid right circular cylinder are in the ratio 7:3 and its volume is 12474 cm³. What is the total surface area of the cylinder? (Use π = \(22\over7\))

A one-meter pipe is made with an inner diameter equal to the outer radius. How much material (in cubic units) is required to make the pipe, if it can hold \(\frac{88}{7}\) cubic meters of water in it?

The radii of the two circular faces of the frustum of a cone are 15 cm and 6 cm. If the height of the frustum is 14 cm, what is the volume in cubic cm?

A drainage tile is a cylindrical shell 42 cm long. The inside and outside diameters are 8 cm and 14 cm, respectively. What is the volume (in cm²) of clay required for the tile? \(( {{Use π={{22} \over 7}}})\)

A carpenter wants to carve a sphere from a solid cylinder of wood. The cylinder has a radius of 21 cm and a height of 28 cm. What is the maximum radius of the sphere that can be carved from the cylinder?

A temple top is a hollow hemispherical dome with an inner radius of 2 units and an outer radius of 3 units. How much concrete (in cubic units) is used to make the top of the temple?

A hemispherical bowl of internal diameter 18 cm contains water. This water is to be filled in cylindrical bottles of diameter 6cm and height 3 cm. The number of bottles required to empty the bowl is:

An open water drum is in the form of a cylinder. The height of the drum is 7 m, and its internal diameter is 21 m. Find the area (in m²) that needs to be painted if one wants to paint the inside of the drum. [Take π = \(22 \over 7\)]

A sphere with an inner radius of 7 cm is fully filled with a chemical costing Rs.24 per cm³. What will be the cost of the chemical (in Rs.), if 50% is taken from the sphere?

A hemispherical bowl of internal radius of 12 cm contains a liquid. This liquid is to be filled into conical shaped small bottles of base diameter 3 cm and height 4 cm. How many same type of bottles will be needed to empty the bowl?

The volume of a cylinder of height 32 cm and base diameter 36 cm is equal to the volume of a cone of height 24 cm. The curved surface area (in cm²) of the cone is:

When a cone is sliced by a plane parallel to its base, but not passing its apex, what is the shape of the resulting cross-section?

A solid cylinder of radius 20 units is melted so as to make solid cones with radius 4 units but same height as that of the cylinder. How many such cones can be made?

The ratio of the heights of a right circular cone and a right circular cylinder is 8 : 9 and the ratio of the radii of their bases is 3 : 4. If the volume of the cylinder is 132 cm³, then the volume (in cm³) of the cone is:

The diameter of the base of a conical tent is 28 feet, and the slant height of the cone is 18 feet. Find the area (in ft²) of the 3 canvases that are required for making this tent. Ignore the wastage of canvas. \(\Big(Use \pi = \frac{22}{7}\Big)\)

The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm. If this is melted and recast into a solid right circular cylinder of height \(10\frac{2}{3}\) cm, then the diameter of the base of the cylinder is _______.

A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 154 cm, then find the cost of painting it if the cost of painting is 4 per ₹100 cm² (use \(\pi=\frac{22}{7}\)).

Find the curved surface area of a toy whose shape is hemisphere mounted on one side of the cylinder if the radius is 14 cm and the total height of the toy is 42 cm.

The difference between the outside and the inside surface area of a cylindrical pipe 14 cm long is 44 cm². The pipe is made of 99 cm³ of metal. If R is the outer radius and r is the inner radius of the pipe, then what is (R + r) equal to?