### Surface Areas And Volumes Class 9th Mathematics AP Board Solution

##### Question 1.A closed cylindrical tank of height 1.4 m. and radius of the base is 56 cm. is made up of a thick metal sheet. How much metal sheet is required (Express in square meters)Answer:Given, radius of the base of a cylinder r = 56cm = 0.56mAnd height h = 1.4mTo find the metal sheet required, we need to find the total surface area of the cylinder.Total surface area of the cylinder = 2πr(r + h)= 2 × π × 0.56 × (0.56 + 1.4)= 6.89 ≃ 6.9m2Question 2.The volume of a cylinder is 308 cm3. Its height is 8 cm. Find its later surface area and total surface area.Answer:Given, volume of cylinder = 308 cm3Height = 8cmVolume of the cylinder = πr2h308 = 3.14 × r2 × 8r2 = r = r = 3.5cmlateral surface area = 2πrh= 2 × 3.14 × 3.5 × 8= 175.9≃ 176cm2Total surface area = 2πr(r + h)= 2 × π × 3.5 × (3.5 + 8)= 252.89 ≃ 253cm2Question 3.A metal cuboid of dimension 22 cm. × 15 cm. × 7.5 cm. was melted and cast into a cylinder of height 14 cm. What is its radius?Answer:Given, A metal cuboid of dimension 22 cm. × 15 cm. × 7.5 cm. was melted and cast into a cylinder of height 14 cmAccording to the question the volume remains same after casting the cuboid inti cylinder, i.e. lbh = πr2h.22 × 15 × 7.5 = 3.14 × r2 × 14r2 = r = r = 7.5cmQuestion 4.An overhead water tanker is in the shape of a cylinder has capacity of 616 litres. The diameter of the tank is 5.6 m. Find the height of the tank.Answer:Given, An overhead water tanker is in the shape of a cylinder has capacity of 616 litresAs 1 litre = 0.001 m3the volume of the cylinder = 0.616 m3.Diameter of the cylinder = 5.6 mRadius of the cylinder = = 2.8 mVolume of the cylinder = πr2h.0.616 = 3.14 × 2.82 × h h = 0.025 m= 2.5 cmQuestion 5.A metal pipe is 77 cm. long. The inner diameter of a cross section is 4 cm., the outer diameter being 4.4 cm. (see figure) Find its(i) inner curved surface area(ii) outer curved surface area(iii) Total surface area. Answer:Given, A metal pipe is 77 cm. longInner Diameter = 4cm i.e. r = 2cmOuter diameter = 4.4cm i.e. R = 2.2cm(i) inner curved surface area = 2πrh= 2 × 3.14 × 2 × 77= 967.6cm2(ii) outer curved surface area = 2πRh= 2 × 3.14 × 2.2 × 77= 1063.8cm2(iii) total surface area = 2πrh + 2πrh + 2π(R2 – r2)= 967.6 + 1063.8 + 2 × 3.14 × (2.22 – 22)= 2036.6cm2Question 6.A cylindrical piller has a diameter of 56 cm and is of 35 m high. There are 16 pillars around the building. Find the cost of painting the curved surface area of all the pillars at the rate of 5.50 per 1 m2.Answer:Given, A cylindrical pillar, diameter = 56cm = 0.56m i.e. r = 0.28cmHeight h = 35mNumber of pillars n = 16Curved surface area of a pillar = 2πrh= 2 × 3.14 × 0.28 × 35= 61.54cmCurved surface area of 16 pillars = 16 × 61.54= 984.64cm2Cost of painting = 5.5 × 984.64= 5415.52Question 7.The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to roll once over the play ground to level. Find the area of the play ground in m2.Answer:Given, diameter = 84cm = 0.84m i.e r = 0.42mLength h = 120cm = 1.20mNumber of revolutions n = 500Area of the playground = n × curved surface area of the roller= 500 × 2πrh= 500 × 2 × 3.14 × 0.42 × 1.2= 1582.56m2Question 8.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.Answer:Given, inner diameter of a circular well = 3.5 m i.e. r = 1.75mHeight = 10m(i) curved surface area = 2πrh= 2 × 3.14 × 1.75 × 10= 109.9m2≃ 110cm2(ii) cost of plastering = 40 × 110= 4400Question 9.Find(i) The total surface area of a closed cylindrical petrol storage tank whose diameter 4.2 m. and height 4.5 m.(ii) How much steel sheet was actually used, if of the steel was wasted in making the tank.Answer:(i) Given, diameter = 4.2mRadius = 2.1mHeight = 4.5mTotal surface area = 2πr(r + h)= 2 × 3.14 × 2.1 × (2.1 + 4.5)= 87m2(ii) if of the steel was wasted in making the tank. The sheet used in making the tank = (1− ) × 87= × 87= 79.75m2Question 10.A one side open cylinderical drum has inner radius 28 cm. and height 2.1 m. How much water you can store in the drum. Express in litres. (1 litre = 1000 cc.)Answer:Given, r = 28cmh = 2.1m = 210cmto find the capacity of water ,the volume of the cylinder = πr2h= 3.14 × 282 × 210= 516969.6cm31litere = 1000cm3Hence, the water stored = = 516.9literesQuestion 11.The curved surface area of the cylinder is 1760 cm.2 and its volume is 12320 cm3. Find its height.Answer:Given, curved surface area = 1760cm2Volume = 12320cm3For finding the height of the cylinder,curved surface area = 1760cm22πrh = 1760rh = rh = 280.25 --------(i)volume = 12320cm3πr2h = 12320cm3r × rh = r = from equation (i), r = r = 14cmhence, rh = 280.25h = h = 20cm

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