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Syllabus

a cone of radius 10 cm is divided into two parts by drawing a plane through the midpoint of its axis , parallel to its base . compare the volume of the two parts

An iron sphere of radius 'a' units is immersed completely in water contained in aright circular cone of semi vertical angle 30 degree ,water is drained off from the cone till it's surface toches the sphere.Find the volume of water remaining in cone.

pls help me frnds

a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field , which is 10m in diameter and 2 m deep. If water flows through the pipe at the rate of 3km/hr , in how much time the tank be filled ?

A well of diameter 3m ,dug 14m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4m to form an embankment. Find the height of the embankment.

The height of a cone is 30cm.A small cone is cut off at the top by a plane parallel to the base.If its volume be 1/27 of the volume of the given cone,then what is the height above the base at which the section is made?

Type-I:A cylindrical glass with inner diameter 7 cm and height as 10 cm.Type-II:A cylindrical glass with inner diameter 4 cm and height as 14 cm.Type-III:A cylindrical glass with inner diameter 14 cm and height as 4 cm. He decided to serve the customers in ‘type-I’ of glasses.water is flowing at the rate of 15km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50m long and 44m wide . find the time in which the level of water in the tank will rise by 21 cm

A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9th of the curved surface of the whole cone, find the ratio of the line segments into which the cone's altitude is divided by the plane.

a cylinder , a cone and a hemisphere of equal base have the same height. what is their ratio in their volumes ?

A hemispherical tank , full of water , is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m ?

A cone of maximum size is carved out from a cube of edge 14cm . FInd out the surface area of the cone and of the remaining solid left out after the carved out . Plzz Answer ....

A right triangle whose sides are 15 cm and 20 cm is made to revolve about its hypoteneous.Find the volume and the surface area of the double cone so formed. (Take pie = 3.14

a piece of paper is in the shape of a semi circular region of radius 10 cm. it is rolled to form a right circular cone. what is the slant height of cone?

pls give the solution.

the rainwater from a roof 22m*20m drains into a cylindrical vessel having diameter of base 2 m and height 3.5m . if the vessel is just full , find the rainfall in cm.

pls do this problem in simple method

total surface area of an hollow sphere and hemisphere?

The interior of building is in the form of a cylinder of diameter 4m and height 3.5m ,surmounted by a cone of the same base with vertical angle as a right angle. Find the surface area (curved) and volume of the interior of the building.

If the diameter of a sphere is decreased by 25%, then by what percent its curved area would decrease?

^{2}, what will be the cost to install 20 such lights?the barrel fountain pen cylindrical in shape is 7cm long and 5mm in diameter. a full barrel of ink in the pen is used up in writing 330 words

on an average.

how many words would use up a bottle of ink containing one fifth of a litre?

A sphere of diameter 12 cm is dropped in a right circular cylinder vessel partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 32/9cm. find the diameter of the cylindrical vessel.

a conical tent is made of 4.5 m wide trapalin . vertical height of the conical tent is 4 m and base radius is3 m .find the lenght of the trapalin used ,assuming that 10 % extra material is required for stiching margins and wastage in cutting (take pie = 3.14)

a copper wire 3mm in diameter ,is wound about a cylinder whose length is 12cm , and diameter 10cm so as to cover the csa of the cylinder . find the length and mass of the wire , assuming the density of copper to be 8.88g per cm3

From a solid cylinder of height 15 cm and diameter 7 cm, two conical holes are drilled each of radius 3 cm and height 4 cm. Find the surface area of the remaining solid

a bucket made up of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. find the cost of the bucket if the cost of the metal sheet is Rs. 15 per 100 cm

^{3 }( use pi= 22/7)a manufacturer involved 10 children in colouring playbg top which is shaped like a cone surmounted by a hemisphere . the entire top is 5cm in heigh and the diameter of the to is 3.5cm . find the area they had to paint if 50 playing tops wee given to them.

(a) how is child labour an abuse gfor the society?

(b)what steps can be taken to abolish child labour?

if h,c,v are respectively the height, curved surface area and the volume of a cone.prove that

3 pie v h cube - c2h2 + 9v2 =0

A hemispherical depression is cut-out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

What is the CSA, TSA and volume of a frustum?

experts please help! i'm unable to understand it's 3rd line..

The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14cm long, is 88cm2. If the volune of metal used in making the cylinder is 176cm3, find the outer and inner diameters of the cylinder

a sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with water . the diameter of the cylindrical vessel is 12cm. if sphere is completely submerged in water by how much will the level of water rise?

A conical vessel of radius 6cm and height 8cm is completely filled with water. A spere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

a bucket i sin the form of frustum with the capacity of 12308.8 cm cube.the radii of the top and bottom of circular ends are 12 cm and 20 cm resp.find the hieght of the bucket and also the area of metal sheets used in making the bucket.(use pie=3.14)

A toy is in the form of a cylinder of diameter 2 2 m and height 3.5 m surmounted by a

Two cubes each of side 4cm are joined end to end.Find the surface area of the resulting cuboid

A bucket open at the top is of the form of a frustum of a cone. The diameters of its upper and lower circular ends are 40cm and 20cm respectively. If the total of 17600cm^3 of water can be filled in the bucket, find its total surface area.

A well of diameter 3m, is dug 14m deep The earth taken out of it has been evenly spread all around it to a width of 4m, to form an embankment Find the height of the embankment use pi=22/7

If the diameter of the cross section of the wire is decreased by 5%,how much %will the length be increased so that the volume remains the same

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere (see figure). The diameters of the ends of the frustum are 5 cm and 2 cm , the height of the entire shuttle cock is 7 cm. Find the external surface area. (Take Pie=22/7) .

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes>

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm

^{2}.Given that,

Height (

h) of the conical part = Height (h) of the cylindrical part = 2.4 cmDiameter of the cylindrical part = 1.4 cm

Therefore, radius (

r) of the cylindrical part = 0.7 cmTotal surface area of the remaining solid will be

= CSA of cylindrical part + CSA of conical part + Area of cylindrical base

The total surface area of the remaining solid to the nearest cm

^{2}is 18 cm^{2}.Why C.S.A. of cone is added instead of subtracting(cause we have to find T.S.A. of remaining part)???

plz explain

An iron sphere of radius 'a' units is immersed completely in water contained in a right circular cone of semi-vertical angle 30 , water is drained off from the cone till its surface touches the sphere. Find the volume of water remaining in the cone.

The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8m, surmounted by a cone whose vertical angle is a right angle. Find the area of the surface and volume of the building.

in cutting four equal circles,the largest,out of a square piece of cardboard of each side 10cm,how many square cm must necessarily be wasted

A solid right cone of diameter 14 cm and height 4 cm is melted to form a holow hemisphere .If the external diameter of the hemisphere is 10 cm,find its internal diameter.Also find the total surface area of the hemisphere

The height of right circular cone is trisected by two plane parallel to its base. Show that the volume of the three propotion from top are in ratio 1:7:19.

(i) What is the height of conical tent ?

(ii) How much space is occupied by each student in the tent ?

A swimming pool is filled by 3 pipes with uniform flow, The first two pipes operating simultaneously, fill the pool in the same time during which the pool is filled by the 3

^{rd}pipe alone. The 2^{nd}pipe fills the pool 5 hours faster than the 1^{st}pipe & 4 hours slower than the 3^{rd}pipe. Find the time required by each pipe to fill the pool separately.Water is flowing at 14.4 km/hr through a pipe of diameter 14cm into a conical tank which has base radius 1.4m. Find the time in which the level of water rises in the tank by 60cm.

cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq. dm is rs.237.60 . the heigth of the tank is 6 times the radius of the base of tank . find its volume correct to two decimal point...? and is que. in easy

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).

t can be observed that

Radius (

r) of cylindrical part = Radius (r) of hemispherical part =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 = Vol. of cylindrical part + 2 × Vol. of hemispherical part

Volume of 45 gulab jamuns == 1,127.25 cm

^{3}Volume of sugar syrup = 30% of volume

plz tell me why it is voulume of gulab jamun is taken to find the sugar suyrup. why we can't take area of gulab jamun in the place volume because container contain gulab jamun we can take their area and then the volume of container. im not able to understand the question. please try to explain with proper diagram.

Water is flowing at the rate of 3km/hr through a circular pipe of 20cm internal diameter into a circular cistern of diameter 10m and depth 2m.In how much time will the cistern be filled? Also, plzz tell that here what is meant by cistern?????

a bicycle wheel makes 75 revolutions per min. to maintain a speed of 8.91km/hr. find the diameter of the wheel..??

A cylindrical copper rod of diameter 1 cm and length 8 cm is drawn into a cylindrical wire of length 18 m and of unifiorm thickness. Find the thickness of the wire.

A n agricultural field is in the form of a rectangle of length 20m and width 14m.A pit 6m long and 3m wide and 2.5m deep is dug in the corner of the field and the earth taken out of thre pit is spread uniformly over the remaining area of the field.find the extent to which the level of the field has been raised..

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m

^{2}. (Note that the base of the tent will not be covered with canvas.)find the area of the shaded region where ABCD is a square of side 14cm . ( four equal circle inside the square) . And please explain me how the radius is obtained .

the derivatio of the formula of frustum of cone

An overhead tank has been constructed to supply water to a village with a population of 3140 at the rate of 25litres per head per day.. water is pumped into it through a pipe of diameter 10cm, the rate of flow being 4m per sec. how long will it take to fill the tank every morning.. pie= 3.14

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm

^{2}. [Take π = 3.14]A conical tent with base radius 7 m and height 24 m is made from 5m wide canvas. Find the length of the canvas used

in one fortnight of a given month ,there was a rainfall of 10cm in a river valley .if the area of the valley is 97280 km sq. ,show that the total rainfall was approx. equivalent to the addition to the normal water of the three rivers each ,1072 km long ,75m wide and 3m deep.

PLEASE HELP THIS ANSWER IS NOT AVAILABLE ON MERITNATION NCERT SOLUTION.

How to derive the formula for voulume of frustum of a cone?

- How to derive the relation bnetween the orginal cone radius / height to the portion of the cone that is removed?

a. Water stands at half the height of the vessel

b. Water stands up to the top of the vessel

c. Water stands at 3/4 of the height of the vessel

d. Water overflows out of the vessel

Please show the claculation also

Water is flowing through a cylindrical pipe, of internal diameter 2cm, into a cylindrical tank of base radius 40cm, at the rate of 0.4m/s. Determine the rise in level of water in the tank in half an hour.

^{3}. find the time required for filling a cylindrical vessel completely having height 7cm and diameter 8cm. also find how many times the vessel can be filled in 3hours 40minutes...???here my answer is:

1) its takes 11minutes to fill the vessel completely

2) we can fill the vessel 20 times in 3hours 40minutes

please see if my answer is correct....

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6cm??(please explain step-wise) :))the conical part is 12 cm. the base of the conical portion has a diameter of 10 cm . If

the conical portion is to be painted red and the base portion green, find the area of the

rocket to be paint. Please no link

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream

A solid toy is in the form of a hemisphere surmounted by a right circular cone.Height of the cone is 2cm and the diameter is 4cm. If a right circular cylinder circumscribes the solid,find how much more space it will cover.

A metallic bucket is in the shape of frustum of a cone.If the diameters of two circulear ends of the bucket are 45 and 25 cm respectively and total height is 24cm find the area of metallic sheet used to make the bucket.Also find the volume.