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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 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 ?

examples of combination of solids in day to day life. could u give some 25 to 50 objects. example like ice cream and capsule

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.

corresponding sides.

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?

Q15.Use the following information to answer the next question.The capacity of a tub, which is of the shape of the frustum of a cone, is 16720000 cm

^{3}. The respective radii of the upper and lower bases of the tub are 90 cm and 40 cm.What is the slant height of the tub?

60 cm

70 cm

120 cm

130 cm

The volume of the frustum of a cone is given by.

∴ Volume of the tub

Slant height (

l) of the frustum of cone =Thus, the slant height of the tub is 130 cm.

The correct answer is D.

ERROR - The volume should be 1672000 and not 16720000, there is an extra zero in the question.

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

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?

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

The radius of a sphere is rcm.It is divided into two equal parts.The whole surface areas of two parts will be?

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 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

(a) 2:3 (b) 6:9 (c) 4:6 (d) 4:9

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)Please don't provide a link to a similar question, as I know the method, and I just wanted to check my answer.

Thank You.

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

structure made from struts set on large circles. Because of its curved

walls and ceiling, these domes use approximately a third less surface

area to enclose the same volume as a traditional box home.

(a) A hollow model of similar type of a structure is constructed with a

hemisphere mounted on the cylinder.

Figure 1

If height of cylindrical part is 6 cm, and total height of the model is 13 cm, then

find the radius of hemisphere.

(i) 5 cm (ii) 3 cm (iii) 7 cm (iv) 4 cm

(b) A square band of side 17 cm is put outside along the edge of the

hemisphere as shown in figure 1. Find the area of metal sheet required for

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.

Volumes of two spheres is in the ratio 64:125. The ratio of their surface areas is ?Please explain with steps...Thank u!

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

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?

The whole surface area of a rectangular block is 846 sq.cm . Find its dimensions,if they are in the ratio 5:4:3.

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)

if the diameter of cross section of the wire is decreased by 50% how much percent the length be increased so that the volume remains same .

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

the surface areas of two spheres are in the ratio 16:9 the ratios of thgeir volume is

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

a warehouse is used as a granary. is is the shape of a cuboid surmounted by a half-cylinder. the base of the shed is 6m x 14m and its height is 8m. find the surface area of the non-cubiodal part.

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

why are we subtracting in the base area as we know that CSA of hemisphere actually means the area of hemisphere without base

Already the base is excluded as we are adding only CSA of hemisphere then again y minus base area

I don't need answer just y need to add base area

(a) X=10,y=2

(b) X=12,y=8

(c) X=2,y=10

(d) X=20,y=0

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 racing track whose left & right are semicircular. The distance between two inner parallel line segments is 60m & they are each 106 m long, if the track is 10 m width,find

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

2.2 cubic decimeter of metal is to be drawn into a cylindrical wire of diameter 0.05 cm.Find the length of wire.

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

A 15cm long test tube having diameter of 3.6 cm has water upto a height of 6 cm. 20spherical drops ofoil of radius 9mm are dropped into it. what lenght of the test tube remains empty ?

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.

^{3}is (A) 176 (B) 196 (C) 200 (D) 110The 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 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.A solid cuboidal block of metal of dimensions 4.4m x 2.6m x 1m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Determine the length of the pipe.

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.

Plz exlain me the relation between litre ans cm

^{3}and m^{3}.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?????

how to calculate the area of quadrilateral ABCD whose sides are 9m, 40m,28m & 15 m

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 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

A solid sphere of radius 6cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5cm and its height is 32cm, find the uniform thickness.

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 reservoir is in the form of a cuboid. It's length is 20m. If 18 kl of water is removed from the reservoir, the water level goes down by 15cm. Find the width if the reservoir.

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 cylindrical tomb 3.5 m in outer radius has a hemispherical roof. find the cost of painting the tomb's exterior at the rate of rs 2 per m sq if the total height of the tomb is 8 m

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?

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.

wax cylinder of diameter 21cm and height 21 cm is chipped off and shaped to form a cone of maximum volume.the chipped off wax is recast into a solis sphere.find thediameter of the sphere..

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

^{2 }= xyzA 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.