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Solved Examples
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fff Find the volume of the solid in the figure. Given a = 4 cm, b = 6 cm.
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fff A toy is in the shape of a hemisphere surmounted by a cone of equal base diameter of 28 cm. Total height of the toy is 29 cm. Find the volume of the toy in c.c. [π = 227]
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fff An auditorium is constructed as shown. Find the total charges for painting its exterior at the rate of $3 per m2. [Neglect doors & windows.][a = 5 m, b = 7 m, c = 8 m, d = 18 m] fff View Solution
fff A warehouse to store finished industrial goods in boxes is constructed as shown. If one box occupies a space of 2 m3, then how many boxes could be stored in the warehouse?[a = 10, b = 14, c = 16, d = 32].
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fff Concrete blocks as shown are to be made. The rate of making concrete is $34 per cubic feet. Find the total cost for making 434 identical blocks. [Take π = 227, a = 21, b = 44, c = 67.]
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fff A tent has cylindrical shape surmounted by a conical roof. The radius(c) of the base is 24 m. height of the cylindrical and conical portions(b and a) are 4 m and 2 m. Find the volume of the tent. [Take π = 3]
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fff A tent is in the form of a cylinder of diameter(a) 25.6 m and height(c) 2.6 m surmounted by a cone of equal base and height(b) 10.2 m. Find the capacity of the tent and the cost of the canvas at $ 34 per m2. (Take π = 3.14) fff View Solution
fff A cylindrical vessel of diameter a cm and height c cm is fixed symmetrically inside a similar vessel of diameter b cm and height c cm. The total space between the two vessels is filled with cork dust for thermal insulation. How many cubic cm of cork dust will be required? [Take π = 227, a = 30, b= 34, c = 63.] fff View Solution
fff Find the volume of the solid in the figure, if a = 6 cm, b = 7 cm and c = 22 cm. [Take π = 3] fff View Solution
fff Find the volume of the solid in the figure. Given a = 24 cm, b = 3 cm.
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fff Find the volume of the box, given a = 20, b = 21, c = 29. fff View Solution
DD  Find the volume of the solid obtained by revolving the figure by 360° about y-axis. Given OA = OB = CD = 3 cm, BC = 18 cm [Take π = 3.]  DD View Solution
DD  A toy is in the form of a cone mounted on a hemisphere of same radius. The diameter(a) of the base of the conical portion is 24 cm. The height(h) of the toy is 28 cm. Determine the surface area of the toy.
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DD  A solid is composed of a cylinder with hemispherical ends. If the total length of the solid is 78 cm and the radius of each of the hemispherical ends is 14 cm, then find the cost of polishing the surface area at the rate of ¢5 per cm2. [Take π = 227]
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DD  What is the total surface area of the figure?[Given a = 15 cm, b = 25 cm, c = 29 cm.]  DD View Solution
DD  What is the surface area of the figure?[Given a = 14 mm, b = 19 mm, c = 18 mm.]
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DD  A right triangle, whose perpendicular sides are 45 cm and 60 cm is made to revolve about its hypotenuse. Find the surface area of the solid formed. [π = 3.14]  DD View Solution
DD  A right triangle, whose perpendicular sides are 60 cm and 80 cm is made to revolve about its hypotenuse. Find the volume of the solid formed.  DD View Solution
DD  An isosceles trapezoid of parallel sides 48 in. and 24 in. is revolved about its longer side. The non-parallel side is 20 in. each. Find the volume of the solid so formed. [Take π = 3.14]
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DD  David sells cone ice creams. An empty cone has a vertical length of 8 cm and a diameter of 10 cm. He sells 150 ice creams on a day, and charges $6 for an icecream. Calculate the additional income he would earn if the dimensions of the cone were reduced by 0.5 cm each, assuming that he does not change the price and sells all the ice creams with him.  DD View Solution
DD  An isosceles trapezoid of parallel sides 84 in. and 42 in. is revolved about its longer side. The non-parallel side is 35 in. each. Find the surface area of the solid so formed.[π = 3.14]  DD View Solution
DD  A vessel is in the shape of a cylinder mounted on a hemisphere of same radius 11 cm. The height of the cylindrical portion is 6 cm. Determine the capacity of the tank in litres. [Take π = 3]
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DD  A cylindrical road roller made of iron is 2 m long. Its internal diameter is 36 cm. The thickness of the iron sheet used to make the roller is 14 cm. Find the mass of the roller, in kg (rounded to one decimal place), if the density of iron is 7.8 g/cubic centimeters. [Take π = 3.]  DD View Solution
DD  Find the volume of the solid in the figure. Given a = 42 cm, b = 27 cm, c = 15 cm.  DD View Solution
DD  A vessel is in the shape of a cylinder mounted on a hemisphere of same radius 13 cm. The height of the cylindrical portion is 8 cm. Determine the capacity of the tank in litres. [Take π = 3]
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DD  Find the volume of the solid in the figure, if a = 2 cm, b = 3 cm and c = 26 cm. [Take π = 3]  DD View Solution
DD  Find the volume of the steel I - beam in cubic feet.  DD View Solution
DD  If the figure shown rotates about y-axis, then the solid formed is
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DD  A right triangle, whose perpendicular sides are 75 cm and 100 cm is made to revolve about its hypotenuse. Find the surface area of the solid formed. [π = 3.14]  DD View Solution
DD  A right triangle, whose perpendicular sides are 105 cm and 140 cm is made to revolve about its hypotenuse. Find the volume of the solid formed.  DD View Solution
DD  A toy is in the shape of a hemisphere surmounted by a cone of equal base diameter of 28 cm. Total height of the toy is 31 cm. Find the volume of the toy in c.c. [π = 227]
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DD  An auditorium is constructed as shown. Find the total charges for painting its exterior at the rate of $3 per m2. [Neglect doors & windows.][a = 15 m, b = 22 m, c = 24 m, d = 47 m]  DD View Solution
DD  A warehouse to store finished industrial goods in boxes is constructed as shown. If one box occupies a space of 2 m3, then how many boxes could be stored in the warehouse?[a = 10, b = 15, c = 16, d = 32].
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DD  Concrete blocks as shown are to be made. The rate of making concrete is $28 per cubic feet. Find the total cost for making 497 identical blocks. [Take π = 227, a = 14, b = 34, c = 51.]
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DD  A tent has cylindrical shape surmounted by a conical roof. The radius(c) of the base is 18 m. height of the cylindrical and conical portions(b and a) are 5 m and 4 m. Find the volume of the tent. [Take π = 3]
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DD  A tent is in the form of a cylinder of diameter(a) 11.2 m and height(c) 1.1 m surmounted by a cone of equal base and height(b) 4.5 m. Find the capacity of the tent and the cost of the canvas at $ 39 per m2. (Take π = 3.14)  DD View Solution
DD  A cylindrical vessel of diameter a in. and height c in. is fixed symmetrically inside a similar vessel of diameter b in. and height c in.. The total space between the two vessels is filled with cork dust for thermal insulation. How many cubic in. of cork dust will be required? [Take π = 227, a = 24, b= 28, c = 49.]  DD View Solution
DD  Find the volume of the solid in the figure. Given a = 24 in., b = 4 in..
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DD  Find the volume of the box, given a = 8, b = 9, c = 15.  DD View Solution
DD  Find the total surface area of the solid formed by rotating the figure by 360° about y-axis.  DD View Solution
DD  Find the volume of the solid obtained by revolving the figure by 360° about y-axis. Given OA = OB = CD = 4 in., BC = 16 in. [Take π = 3.]  DD View Solution
DD  A toy is in the form of a cone mounted on a hemisphere of same radius. The diameter(a) of the base of the conical portion is 36 cm. The height(h) of the toy is 42 cm. Determine the surface area of the toy.
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DD  A solid is composed of a cylinder with hemispherical ends. If the total length of the solid is 104 in. and the radius of each of the hemispherical ends is 21 in., then find the cost of polishing the surface area at the rate of ¢4 per in.2. [Take π = 227]
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DD  An isosceles trapezoid of parallel sides 60 cm and 30 cm is revolved about its longer side. The non-parallel side is 25 cm each. Find the volume of the solid so formed. [Take π = 3.14]
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DD  An isosceles trapezoid of parallel sides 132 cm and 66 cm is revolved about its longer side. The non-parallel side is 55 cm each. Find the surface area of the solid so formed.[π = 3.14]  DD View Solution
DD  A metallic solid shown in Figure 1 is melted to make a number of bullets of the shape shown in Figure 2. How many bullets were made? (Round the answer to nearest whole number.) [Given r1 = 4, l1 = 4, l2 = 9, r2 = 3 and h = 4.]  DD View Solution
DD  A cylindrical road roller made of iron is 3 m long. Its internal diameter is 32 cm. The thickness of the iron sheet used to make the roller is 10 cm. Find the mass of the roller, in kg (rounded to one decimal place), if the density of iron is 7.8 g/cubic centimeters. [Take π = 3.]  DD View Solution
DD  Find the volume of the solid in the figure. Given a = 78 cm, b = 45 cm, c = 33 cm.  DD View Solution
DD  What is the total surface area of the figure?[Given a = 21 in., b = 35 in., c = 38 in..]  DD View Solution
DD  What is the surface area of the figure?[Given a = 8 mm, b = 17 mm, c = 16 mm.]
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DD  David sells cone ice creams. An empty cone has a vertical length of 9 cm and a diameter of 6 cm. He sells 180 ice creams on a day, and charges $5 for an icecream. Calculate the additional income he would earn if the dimensions of the cone were reduced by 0.5 cm each, assuming that he does not change the price and sells all the ice creams with him.  DD View Solution