Surface Areas and Volumes| NCERT Solutions| Class 9

NCERT Solutions of  Chapter: Surface Area and Volumes. NCERT Solutions along with worksheets and notes for Class 9.

Exercise 13.1

(1) A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine:

(i) The area of the sheet required for making the box.

(ii) The cost of sheet for it, if a sheet measuring 1 m2 costs Rs 20.

 

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(2) The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m2.

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(3) The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per m2 is Rs 15000, find the height of the hall.

[Hint: Area of the four walls = Lateral surface area]

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(5) A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

(ii) Which box has the smaller total surface area and by how much?

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(6) A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i) What is the area of the glass?

(ii) How much of tape is needed for all the 12 edges?

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(2) It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?

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(3) A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm (figure below). Find its

(i) inner curved surface area,

(ii) outer curved surface area

(iii) total surface area.

Diagram of Question 3 of Exercise 13.2 of Chapter Surface Areas and Volumes

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(4) The diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolutions to move once to level a playground. Find the area of the playground in m2.

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(5) A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs 12.50 per m2.

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(6) Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find the height.

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(7) The inner diameter of a circular well is 3.5 m. it is 10 m deep. Find

(i) its inner curved surface area.

(ii) the cost of plastering this curved surface at the rate of Rs 40 per m2.

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(8) In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

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(10) In figure below, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.

 

Diagram of Question 10 of Exercise 13.2 of Surface Areas and Volumes

 

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(11) The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

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Exercise 13.3

(1) Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

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(2) Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

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(3) Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.

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(4) A conical tent is 10 m high and the radius of its base is 24 m. Find

(i) slant height of the tent.

(ii) cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.

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(6) The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white – washing its curved surface at the rate of Rs 210 per 100 m2.

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(7) A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

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(2) Find the surface area of a sphere of diameter:

(i) 14 cm   (ii) 21 cm    (iii) 3.5 m

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(4) The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

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(5) A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin – plating it on the inside at the rate of Rs 16 per 100 cm2.

 

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(6) Find the radius of a sphere whose surface area is 154 cm2.

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(7) The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

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(8) A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

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(9) A right circular cylinder just encloses a sphere of radius r (Figure below). Find

(i) surface area of the sphere,

(ii) curved surface area of the cylinder,

(iii) ratio of the areas obtained in (i) and (ii).

Diagram of Question 9 of Exercise 13.4 of Chapter Surface Areas and Volumes

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(2) A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000 l)

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(3) A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

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(4) Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.

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(5) The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

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(8) A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

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(9) A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

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(2)The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.

 

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(3) A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

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(5) It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m2, find

(i) inner curved surface area of the vessel,

(ii) radius of the base,

(iii) capacity of the vessel.

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(6) The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

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(7) A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filed in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

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(8) A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

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(2) Find the capacity in litres of a conical vessel with

(i) radius 7 cm, slant height 25 cm   (ii) height 12 cm, slant height 13 cm

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(4) If the volume of a right circular cone of height 9 cm is 48  cm3, find the diameter of its base.

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(5) A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

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(6) The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find

(i) height of the cone      (ii) slant height of the cone

(iii) curved surface area of the cone

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(7) A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

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(8) If the triangle ABC in the question 7 above is resolved about the side 5 cm, then find the volume of the solid so obtained. Find also the radio of the volumes of the two solids obtained in questions 7 and 8.

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(9) A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

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Exercise13.8

(1) Find the volume of a sphere whose radius is

(i) 7 cm    (ii) 0.63 m

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(2) Find the amount of water displayed by a solid spherical ball of diameter

(i) 28 cm    (ii) 0.21 m

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(3) The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3?

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(4)The diameter of the moon is approximately one – fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

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(5)How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

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(6) A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

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(7) Find the volume of a sphere whose surface area is 154 cm2.

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(8) A dome of a building is in the form of a hemisphere. From inside, it as white – washed at the cost of Rs 498.96. If the cost of white – washing is Rs 2.00 per square metre, find the

(i) inside surface area of the dome,   (ii) volume of the air inside the dome.

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(9) Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S. Find the

(i) radius r of the new sphere,    (ii) ratio of S and S.

 

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(10) A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?

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Exercise 13.9 (Optional)

(1) A wooden bookshelf has external dimensions as follows: Height=110cm, depth = 25 cm, Breadth = 85 cm, (see figure below). The thickness of the planks is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.

 

Figure of question 1 of exercise 13.9 of chapter Surface areas and volumes

 

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(2) The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in fig below. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm2.

 

Figure of question 2 of exercise 13.9 of chapter Surface areas and volumes

 

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(3) The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

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Helping Topics

Mensuration

Worksheet Class 9

 

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