Chapter 13 – Surface Areas and Volumes
Hanumappa and his wife Gangamma are busy making Jaggery out of sugar-cane. They have processed the sugar cane juice to make the molasses which is poured into moulds of the shape shown in the figure. It will be cooled to solidify in this shape to be sent to the market. Each mould is in the shape of a frustum of a cone having the diameters of its two circular ends as 30cm and 35cm and the height of the mould is 14cm. If each cm^3 of molasses weighs about 1.2gm, find the weight of molasses that can be poured into each mould (Take π=22/7)
06
Oct
Hanumappa and his wife Gangamma are busy making Jaggery out of sugar-cane. They have processed the sugar cane juice to make the molasses which is poured into moulds of the shape shown in the figure. It will be cooled to solidify in this shape to be sent to the market. Each mould is in the [...]
The radii of the ends of frustum of a cone 45 cm high are 28 cm and 7 cm. Find its volume, the curved surface area and the total surface area.
06
Oct
The radii of the ends of frustum of a cone 45 cm high are 28 cm and 7 cm. Find its volume, the curved surface area and the total surface area. the curved surface area and the total surface area. The radii of the ends of frustum of a cone 45 cm high are 28 [...]
A hemispherical tank full of water is emptied by a pipe at the rate of 3 7/4 litres per second . How much time will it take to half empty the tank, if the tank is 3 metres in diameter? (Take π = 22/7)
06
Oct
A hemispherical tank full of water is emptied by a pipe at the rate of 3 7/4 litres per second . How much time will it take to half empty the tank, if the tank is 3 metres in diameter? (Take π = 22/7) A hemispherical tank full of water is emptied by a pipe [...]
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
06
Oct
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness [...]
Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank). Which is in the shape of a cuboid. The sump has dimensions 1.57m×1.44m×0.95m. The overhead tank has its radius of 60cm and its height is 95cm. Find the height of the water, left in the sump after the overhead tank has been completely filled with water from a sump which had been full. Compare the capacity of the tank with that of the sump (Use π=22/7)
06
Oct
Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank). Which is in the shape of a cuboid. The sump has dimensions 1.57m×1.44m×0.95m. The overhead tank has its radius of 60cm and its height is 95cm. Find the height of the water, [...]
A cone of height 24cm and radius of base 6cm is made up modelling clay. A child reshapes it in the form of sphere. Find the radius of the sphere.
06
Oct
A cone of height 24cm and radius of base 6cm is made up modelling clay. A child reshapes it in the form of sphere. Find the radius of the sphere. A cone of height 24cm and radius of base 6cm is made up modelling clay. A child reshapes it in the form of sphere. Find [...]
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volume of the cylinder and toy. (Take π=3.14).
06
Oct
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volume of the [...]
A juice seller was serving his customers using glasses as shown in figure. The inner diameter of the cylindrical glass was 5cm,but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10cm, find the apparent capacity of the glass and its actual capacity.(Use π=3.14)
06
Oct
A juice seller was serving his customers using glasses as shown in figure. The inner diameter of the cylindrical glass was 5cm,but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10cm, find the apparent capacity of the glass and [...]
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A juice seller was serving his customers using glasses as shown in figure. The inner diameter of the cylindrical glass was 5cm ,
but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10cm ,
find the apparent capacity of the glass and its actual capacity.(Use π=3.14) ,
Shanta runs an industry in a shed that was in the shape of a cuboid surmounted by half-cylinder. If the base of the shed is 7 m×15 m and height of the cuboidal portion is 8 m, find the volume of the air that the shed can hold. If the industry requires machinery which would occupy a total space of 300 m^3 , and there are 20 workers each of whom would occupy 0.08 m^3 space on an average, how much air would be in the shed when it is working. (Take π = 7/22)
06
Oct
Shanta runs an industry in a shed that was in the shape of a cuboid surmounted by half-cylinder. If the base of the shed is 7 m×15 m and height of the cuboidal portion is 8 m, find the volume of the air that the shed can hold. If the industry requires machinery which would [...]
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and there are 20 workers each of whom would occupy 0.08 m^3 space on an average ,
find the volume of the air that the shed can hold. If the industry requires machinery which would occupy a total space of 300 m^3 ,
how much air would be in the shed when it is working. (Take π = 7/22) ,
Shanta runs an industry in a shed that was in the shape of a cuboid surmounted by half-cylinder. If the base of the shed is 7 m×15 m and height of the cuboidal portion is 8 m ,
Mayank made a bird-bath for his garden in the shape of cylinder with a hemispherical depression at one end as shown in figure. The height of the hollow cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take π=22/7)
06
Oct
Mayank made a bird-bath for his garden in the shape of cylinder with a hemispherical depression at one end as shown in figure. The height of the hollow cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take π=22/7) Two cubes each of volume 64 cm^3 [...]