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Find the radius of the sphere whose surface area is \(154\ cm^2 \).
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The dimensions of a box are \(12\ cm \times 4\ cm \times 3\ cm\). Find the length of the longest rod which can be placed in this box.
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length of longest rod
How many cubes of sides \(3\ cm \) can be cut from a cuboid measuring \(18\ cm \times 12\ cm \times 9\ cm\)?
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Number of cubes
Find the height of the cone whose volume is \(1570\ cm^3\) and area of base is \(314\ cm^2\).
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The circumference of the edge of a hemispherical bowl is 132 cm. Find the capacity of the bowl.
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If the lateral surface area of a cylinder is \(94.2\ cm^2\), and its height is \(5\ cm\), then find the radius of its base.
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Two cubes each of edge 4 cm are joined face to face. Find the surface area of the resulting cuboid.
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Surface area
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions?
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Area = CSA no. of revolution
CSA
Area covered
The largest possible sphere is carved out from a solid cube of side 7 cm. Find the volume of the sphere.
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Radius of the sphere
Volume
A right circular cone is 3.6 cm high and has base radius 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.
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Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height.
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Volume of sphere
Volume of cylinder
Volume of cone
Ratio
A cone and a sphere have equal radii and equal volume. What is the ratio of the diameter of the sphere to the height of the cone?
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What is the ratio of the volume of a cube to that of a sphere which will fit exactly inside the cube?
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A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. Find the total surface area of the shape so formed.
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Height of new cylinder
A solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone. Find the curved surface area and the total surface area of the shape thus formed.
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A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have ? Find the surface area of the solid.
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Greater diameter = side of cube = 7 cm
Surface area of cube
Greater area of base of hemisphere
CSA of hemisphere
A solid cube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the given cube and that of one of the cuboids.
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Length of each resulting cuboids
Let the side of the cube
Find the capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure.
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Capacity of vessel = Capacity of cylinder – capacity of hemispher
A spherical iron ball of radius r is melted to make 8 new idential balls. Find the radius of each new ball.
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Radius of new ball is half of radius of spherical ball
The circumference of the base of a 9 m high wooden solid cone is 44 m. Find the volume of the cone.
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Volume of cone
Radius of a cone is 4 cm. Find the height of the cone so that its volume may be equal to that of a sphere of radius 2 cm.
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Volume of sphere
A/Q
The height of a cone is 5 cm. Find the height of another cone whose volume is sixteen times its volume and radius equal to its diameter.
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Volume
Volume is 16 times
Radius is half
A/Q
If the radii of the ends of a bucket 24 m high are 5 cm and 15 cm, find the surface area of the bucket.
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Surface area of bucket
The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is \(5\sqrt5\ cm \) What is its surface area?
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and
Surface area of cuboid
A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is covered into the water untill it is completely immersed. Find the rise in the water level in the vessel.
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A hemisphere of iron of radius 12 cm is melted and cast into a right circular cone of height 54 cm. Find the radius of the base of the cone.
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Substituting the values
we get
Radius of the base of cone
The radius and slant height of a right circular cone are in the ratio of 7 : 13 and its curved surface area is \( 286\ cm^2\). Find its radius \(\left(use\ \pi=\dfrac{22}{7}\right) \)
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Radius
A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.
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Height of cone
Surface area
A solid cone of radius 4 cm and vertical height 3 cm has to be painted from outside except the base. Find the surface area to be painted.
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Three cubes of volume \(64\ cm^3 \) each are joined end to end to form a solid. Find the surface area of the cuboid so formed.
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Side of each cube
Dimensions of cuboid
Surface area
The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, find the height of the frustum.
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The volume of a right circular cylinder of height \(7\ cm \) is \(567\ \pi\ cm^3 \). Find its curved surface area. \(\left(Take\ \pi=\dfrac{22}{7}\right) \).
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Find the number of solid cylindrical structures of radius 7 cm and height 10 cm which can be made from a solid cylinder of radius 7 m and height 10 m.
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A solid cuboidal slab of iron of dimensions \(66\ cm \times 20\ cm \times 27\ cm\) is used to cast an iron pipe. If the outer diameter of the pipe is 10 cm and thickness is 1 cm, then calculate the length of the pipe.
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Volume
outer radius of pipe
Inner radius
volume of pipe
A/Q
The circumference of the circular end of a hemispherical bowl is 132 cm. Find the capacity of the bowl.
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A solid cylinder of radius r and height h is placed over other cylinder of the same height and radius. Find the total surface area of the shape so formed.
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Height of new cylinder
Radius of new cylinder
Total surface area
How many coins \(1.75\ cm \) in diameter and 2 mm thick must be melted to form a cuboid of dimensions \(11\ cm \times 10\ cm \times 7\ cm\)? \(\left(Take\ \pi=\dfrac{22}{7}\right) \)
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Diameter , radius
Volume of coin
Volume of cuboid
Number of coins
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 m of standing water is needed?
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Volume of canal
Area irrigated
Area irrigated hectares
The total surface area of a right circular cone is \(90\ \pi\ cm^2 \). If the radius of base of the cone is \(5\ cm \), find the height of the cone.
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The radius of the base and the height of a right circular cylinder are in the ratio of 2 : 3 and its volume is 1617 cu.cm. Find the curved surface area of the cylinder \(\left(use\ \pi=\dfrac{22}{7}\right) \).
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Surface area
A solid is hemispherical at the bottom and conical above. If the curved surface area of the two parts are equal, then find the ratio of the radius and height of the conical part.
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A spherical solid ball of diameter 21 cm is melted and recast into cubes, each of side 1 cm. Find the number of cubes thus formed. \(\left(use\ \pi=\dfrac{22}{7}\right) \)
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Volume of sphere
Volume of cube
A/Q
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. \(\left(Take\ \pi=\dfrac{22}{7}\right) \)
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Radius of hemisphere
Hight of cylinder
Inner surface area
The surface area of a sphere is \(616\ cm^2\). Find its radius.
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A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.
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Volume of cone
Volume of cylinder
Height and radius are equal
Ratio
The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum.
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From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.
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Volume of cube
Volume of conical
Volume
The cones with same base radius 8 cm and height 15 cm are joined together their bases. Find the surface area of the shape so formed.
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Surface area of the shape = CSA of cone 1 + CSA of cone 2
Surface area
A spherical bowl of internal diameter 36 cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?
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Volume of hemisphere
Volume of cylindrical bottle
A/Q
A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.
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TSA of cone
Surface area of cube
Surface area of remainings solid