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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

a triangle is formed by joining mid points of alternate sides of a regular hexagon. what is the ratio of area of triangle so formed and area of regular hexagon

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 ?

Q a biscuit laid into a rectangular tray of length 2.5m and breadth 1m out of this 1000 biscuits of radii 2.8cm each are cut out from a circular disc .how much area of ring is left wasted .

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?

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 ....

what is meant by surface area

is it tsa or csa??????

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

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

Four spheres each of radius 10 cm lie on a horizontal table so that the centres of the spheres form a square of side 20 cm. A fifth sphere also of radius 10 cm is placed on then so that it touches each of these spheres without disturbing them . Find that how many cms above the table is the centre of the fifth sphere ?

total surface area of an hollow sphere and hemisphere?

a godown building is in a form where vertical cross-section paralell to the width side of the building is a rectangle 7m*3m, mounted by a semi-circle of radius 3.5m. the inner measurements of the cuboidal portion of the building are 10m*7m*3m. find the volume of the godown and the total interior surface area excluding the floor(base)

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

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

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 bicycle wheel makes 75 revolutions per minute to maintain spedd of 8.91km/hr find the diameter of wheel??

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 toy in the shape of solid cylinder surmounted by a conical top.If the height of the diameter of the cylinder path are 21cm and 40cm respectively and height of the cone is 15cm.Find the total surface area of the toy. use 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

PQRS is a square of side length 12 and XPQ is a triangle constrcted on QR ouwardly such that XQ = XR. If areathe figure,of the figure PQXRS is 192, then area of the figure (PRX) lies b/w

1. 50 - 60

2. 60 - 70

3. 70 - 80

4. 80 - 90

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)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.

150 marbles each of diameter 1.4cm are dropped in a cylinderical vessel of diameter 7cm containing some water which are completely immersed in water. find the rise in the level of water in the vessel

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

how can you find the surface area of a cube,cuboid,cone and a pyramid by using flat cut outs?

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?

Two water taps together can fill a tank in 6 hours.the tap of larger diameter takes 9 hours less than the smaller one to fill the tank seperately. find the time in which each tap can seperately fill the tank?

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?

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 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 cylindrical pipe has inner diameter 7cm and water flows through it at 192.5litres per min. Find the rate of flow in kilometres per hour.

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

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 -2 is a root of the quadratic equation x2 -px -5 =0 and the quadratic equation x2 +px +k =0 has equal roots ,find the value of k.

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 cyclist cycles non-stop from A to B, adistance of 14 kmat a certain average speed. If his average speed reduces by 1kmperhe takes 1/3hr more to cover the same distance. find the original speed

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>

Q.4. As shown in the figure diameter of outer circle is 12 cm. Ratio of shaded area of upper semi circle to

that of the shaded area in the lower semicircle.

(A) 1 : 1

(B) 11 : 3

(C) 4 : 3

(D) 8 : 27

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

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.

A Hemispherical tank full of water is emptied by a pipe at the rate of 3

^{4}/7 litres per second. how much time will it take to empty half the tank, if it is 3m in diamterThe height of cone is 30cm. A small cone is cut off at the topby a plane parallel to the base. If its volume is {1/ 27}th of the volume of given cone. At what height above the base is the section made

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.

A solid is in the shape of a cone mounted on a hemisphere of same base radius,if the curved surface areas of the hemispherical part and the conical part are equal then find the ratio of the radius and the height of the conical part.

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

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.

the diameter of a cycle wheel is 21 cm. how many revolutions willl it make to travel 1.98 km? plsssssssss answer soon

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.

How many cubic centimeter of iron is required to construct an open box whose external dimensions are 36cm,25cm, and 16.5 cm provided the thickness of the iron is 1.5cm. If one cubic cm of iron weighs 7.5g find the weight of the box.

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.)A juice seller has three types of glasses of inner diameter 5cm and height

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

Q). A solid rectangle piece of iron measures $5m\times 6m\times 2m$. Find the weight of the piece in kg if $1{m}^{3}$ of iron weighs 50 gms. also find the cost of piece of iron at the rate of Rs. $750/kg$.

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 toy is in the form of a cone mounted on a hemisphere of diameter 7cm. If the base radii of both hemisphere and cone is same and the total height of the toy is 14.5 cm, find the volume and total surface area of toy

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.

A solid metal cylinder of radius 14 cm and height 21 cm is melted and recast into spheres of radius 3.5 cm.Calculate the number of spheres that can be made.

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 survey carried by the school social club for the students come by car in school , (x-9)/2 cars carry one kid , under root x carry two students , x/7 carry three students and under root x/7 carrry four tudents if the total number of students is 59 , find the total number of cars used by 59 students .

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.

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) :))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 cube is inscribed in a hemisphere of radius R , such that four of its vertices lie on the base of the hemisphere and the other four touch the hemispherical surface of the sphere of the sphere. Find the volume of cube.

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.