Advertisements
Advertisements
प्रश्न
A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the given figure). Use [π = 22/7]
उत्तर
It can be observed that
Radius (r) of cylindrical part = Radius (r) of hemispherical part = `2.8/2` = 1.4 cm
Length of each hemispherical part = Radius of hemispherical part = 1.4 cm
Length (h) of cylindrical part = 5 − 2 × Length of hemispherical part
= 5 − 2 × 1.4
= 2.2 cm
Volume of one gulab jamun = Volume of cylindrical part + 2 × Volume of hemispherical part
= `pir^2h+2xx2/3pir^3 = pir^2h+ 4/3pir^3`
= `pixx(1.4)^2 xx 2.2 + 4/3pi (1.4)^2`
= `22/7 xx 1.4 xx 1.4xx2.2+4/3xx22/7xx1.4xx1.4xx1.4`
= 13.552 + 11.498
= 25.05 cm3
Volume of 45 gulab jamuns = 45 × 25.05 = 1,127.25 cm3
It can be observed that
Radius (r) of cylindrical part = Radius (r) of hemispherical part
= `2.8/2`
= 1.4 cm
Length of each hemispherical part = Radius of hemispherical part
= 1.4 cm
Length (h) of cylindrical part
= 5 − 2 × Length of hemispherical part
= 5 − 2 × 1.4
= 2.2 cm
Volume of sugar syrup = 30% of volume
= `30/100 xx 1127.25`
= 338.175 cm3
= 338 cm3
APPEARS IN
संबंधित प्रश्न
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
50 circular plates each of diameter 14cm and thickness 0.5cm are placed one above other to form a right circular cylinder. Find its total surface area?
A conical flask is full of water. The flask has base radius r and height h. The water is poured into a cylindrical flask of base-radius mr. Find the height of water in the cylindrical flask.
A cylindrical vessel of diameter 14cm and height 42cm is fixed symmetrically inside a similar vessel of diameter 16cm and height 42 . cm The total space between two vessels is filled with cork dust for heat insulation purpose. How many cubic cms of cork dust will be
required?
A bucket made up of a metal sheet is in form of a frustum of cone of height 16cm with diameters of its lower and upper ends as 16cm and 40cm. find the volume of bucket. Also find cost of bucket if the cost of metal sheet used is Rs 20 per 100 cm2
The rain water from a 22 m × 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills `4/5` th of the cylindrical vessel, then find the rainfall in centimetre.
The volume of a right circular cylinder with its height equal to the radius is `25"1"/7` cm3. Find the height of the cylinder.
A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.
Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is `12sqrt(3)` cm. Find the edges of the three cubes.
The volumes of two cubes are in the ratio 1 : 27. The ratio of their surface area is
The heights of two circular cylinders of equal volume are in the ratio 1 : 2. The ratio of their radii is
A hollow metallic sphere with external diameter 8 cm and internal diameter 4 cm is melted and moulded into a cone of base radius 8 cm. The height of the cone is
A solid metal cone with base radius 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls formed.
A hemispherical bowl of internal diameter 30 cm is full of a liquid. This liquid is poured into cylindrical bottles of diameter 5 cm and height 6 cm each. How many bottles are required?
A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm. Find the rise in the level of water.
The volume of a right circular cylinder is 345 cm³. Then, the volume of a right circular cone whose radius of the base and height is the same as of circular cylinder will be ______.
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is ______.
Two solid cones A and B are placed in a cylinderical tube as shown in the figure. The ratio of their capacities are 2:1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder
A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10 cm. If the mortar occupies `1/10` th of the volume of the wall, then find the number of bricks used in constructing the wall.
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?
