# Volume and Surface Area - Aptitude test questions and answers

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## Volume and Surface Area - Aptitude test questions and answers

Q1. Find the volume , if the surface area of a cube is 150 sq. cm?

A)25 cu.cm
B)125 cu.cm
C) 5 cu. cm.
D)120cu. cm

Q2. If the volume of a cube is 512 cu.cm, then the Surface area and the length of the diagonal of the cube is

A)264 sq.cm and 13.85 cm
B) 164 sq.cm and 18 cm
C) 512 sq.cm and 8 cm
D) 128 sq.cm and 7 cm

ANSWER: A)264 sq.cm and 13.85 cm

Q3.Find the height of a Cuboid , if the volume and area of its base is 1240cm3 and 40 sq.cm respectively.

A)31 cm
B)20 cm
C)60cm
D)41cm

Q4. Find the area of base of Cuboid, if the volume and height are 4000cm3 and 50 cm respectively?

A)80 sq.cm
B)40 sq.cm
C)2000 sq.cm
D)1600 sq.cm

Q5.Find the surface of the cuboid if two cubes of each 20cm edge are joined end-to-end?

A)1000cm2
B)2000cm2
C)1600cm2
D)4000cm2

Q6. A paper sheet is of rectangular shape of 24 cm by 13 cm from each of its corners a square of 4 cm is cut off. An open box is made of the remaining sheet, what is the volume of the box.

A) 320 cm3
B) 120 cm3
C) 160 cm3
D) 250 cm3

Q7. Find the lateral surface area of the cylinder, if the volume of a cylinder is 224Πcm3 and height 3.5cm?

A)350 cm2
B)300 cm2
C)175.84 cm2
D)360 cm2

Q8. The radii and height of two cylinders are in the ratio 3:2 and 4:5 respectively. Find the ratio of their volumes

A)9:5
B)18:10
C)21:25
D)8:3

Q9. A cylindrical container of diameter 14 cm and height 6 cm is full of Milk. The Milk is emptied into a rectangular tub of length 33 cm and breadth 14 cm. The height of which Milk rises in the tub is

A)4cm
B)8cm
C)12cm
D) 2cm

Q10.If the surface area of a cube is 294 sq.cm ,then its volume is

A)49 cu.cm
B)343 cu.cm
C) 7cu.cm.
D)214cu. cm

Q11. If the volume of a cube is 64 cu.cm, then the Surface area and the length of the diagonal of the cube is

A) 96 sq.cm and 6.92 cm
B) 164 sq.cm and 18.90 cm
C) 212 sq.cm and 8 cm
D) 88 sq.cm and 7 cm

ANSWER: A) 96 sq.cm and 6.92 cm

Q12. The area of three adjacent faces of a cuboid are a, b and c. If its volume is Z, then which option is correct?

A) Z2 = abc
B) Z3 = abc
C)Z = abc/3
D)None of these

Q13. Find the total surface area of the cylinder, if the volume of a cylinder is 224Πcm3 and height 3.5cm?

A)350.67 cm2
B)722.56 cm2
C)577.76 cm2
D)360.04 cm2

Q14. A hollow cylinder open at both ends is made of steel 2cm thick. What will be the volume of steel used in making the cylinder, if the external diameter is 24cm and the length of cylinder is 55cm.

A)7598.8 cu.cm
B)8500 cu.cm
C)4800 cu.cm
D)3467.80 cu.cm

Q15.What will be the lateral surface area of cone , if its radius and vertical height are 10 cm and 24 cm respectively?

A)816.4cm2
B) 408.2cm2
C)212.8cm2
D)none of these

Q16. How many cm of paper sheet 10cm wide will be required to make a cone, the radius of whose base is 9 cm and whose height is 12cm.

A)45.50
B)24
C)42.39
D)29

Q17. Find the capacity of a Flower pot, if the radii of the ends of a pot of height 12cm are 8 cm and 4cm?

A)1406.72cm3
B)406.34 cm3
C)345 cm3
D)129 cm3

Q18. The radii of two cones are equal. If their slant height are in the ratio 3:2. Then the ratio of their curved surface areas are

A)2:3
B)1:2
C)3:2
D)None of these

Q19. Find the surface area of sphere, if its volume and radius are 38808cm3 and 21cm respectively?

A)5544cm2
B) 1548cm2
C) 544cm2
D)6000cm2

Q20. The surface area of a cube is 384 sq.cm ,what will be the volume of a cube

A)8 cu.cm
B)512 cu.cm
C)64 cu.cm.
D)128 cu.cm

Q21. A cylindrical container of radius 28 m and height 24 m is full of water. The Water is emptied into a swimming pool of length 100 m and breadth 28 m. The height of which Water rises in the swimming pool is

A) 21.12 m
B) 32.21m
C) 19.56m
D) 28.50m

Q22. A hollow cylindrical pipe open at both ends is made of rubber 5cm thick. What will be the volume of rubber used in making the pipe, if the external diameter is 100cm and the length of cylinder is 50cm.

A)74575 cu.cm
B)85000 cu.cm
C)48000 cu.cm
D)34678 cu.cm

Q23.What will be the curved surface area of cone , if its diameter and vertical length are 100 cm and 25 cm respectively?

A)8776.3cm2
B)2214.2cm2
C)1432.8cm2
D)1242.9cm2

Q24. Find the capacity of a Water bucket, if the diameter of the ends of a bucket of height 42cm are 16 cm and 12cm?

A)26024.32cm3
B)14061.34 cm3
C)32345 cm3
D)23129 cm3

Q25.What will be the radius of the sphere, if the number of square cm on the surface of a sphere is equal to the number of cubic cm in its volume.

A)6cm
B)3cm
C)8cm
D)4cm

Q26. What will be radii of hemisphere if the ratio of the volumes of two hemisphere is 216 : 64?

A)6:4
B)64:216
C)4:11
D)none of these

Q27.How many metal sphere each of radius 4cm can be made by melting a big metal sphere whose radius is 16.

A)64
B)16
C)78
D)28

Q28. If the side of a cube is increased by x%, then find increase in percent of its volume .

A)[(1+x/100) 3 -1] *100 %
B) [(1+x/100) 3 -1]%
C) [(1+2x/100) 3 -1]
D)none of these.

ANSWER: A)[(1+x/100) 3 -1] *100 %

Q29. A metal sphere of radius 3cm is drawn into a wire of diameter 44mm. Then find the length of the wire ?

A)9cm
B)30 cm
C)9m
D)30m

Q30. Find the volume, If the surface area of a cube is 2400 sq.cm.

A)4800 cu.cm
B)8000 cu.cm
C)400 cu.cm.
D)20 cu.cm

Q31. If the volume of a cube is 4096 cu.cm, then the Surface area and the length of the diagonal of the cube is

A) 1536 sq.cm and 27.71 cm
B) 1164 sq.cm and 118.90 cm
C) 2212 sq.cm and 18 cm
D) 188 sq.cm and 17 cm

ANSWER: A) 1536 sq.cm and 27.71 cm

Q32. The radii and height of two cylinders are in the ratio 4:5 and 3:2 respectively. Find the ratio of their volumes

A)24:25
B)8:11
C)12:25
D)8:3

Q33. A cylindrical container of diameter 42 m and height 24 m is full of Diesel. The Diesel is emptied into a rectangular pool of length 132 m and breadth 56 m. The height of which Diesel rises in the pool is

A) 22m
B) 18m
C) 9m
D) 4.5m

Q34.What will be the lateral surface area of cone , if its diameter and vertical length are 24 cm and 8 cm respectively?

A)543.34cm2
B) 214.2cm2
C)432.8cm2
D)none of these

Q.35 How many metre of cloth 10 m wide will be required to make a conical tent, the diameter of whose base is 28 m and whose height is 20m.

A)107.30
B)24.5
C)72.39
D)201

Q36. The diameter of two cones are equal. If their slant height are in the ratio 15:11 . Then the ratio of their curved surface areas are

A)15:11
B)2:1
C)3:5
D)1:3

Q37. How many metal balls each of radius 18cm can be made by melting a big metal ball whose radius is 2cm.

A)729
B)81
C)78
D)189

Q38. If the diameter of a sphere is doubled , how does its surface area change?

A)decrease two times
B)increase two times
C)decreases four times
D)increases four times

Q39. Find the length of wire used, if the curved surface of a cylinder is 1000 sq.cm. A wire of diameter 5mm is wound around it, so as to cover it completely?

A)2000cm
B)2400cm
C)3200cm
D)none of these

Q40. Two solid spheres of metal having radius 1.5cm and 2cm are molten and the cast into one big sphere. If the radius of the sphere is x, then find x3 ?

A)11.375 cu.cm
B)12.08 cu.cm
C)13.89 cu.cm
D) none of these

Q41. The paint in a certain container is sufficient to paint an area equals to 5.875m2. How many bricks of dimensions 12.5 cm* 10 cm* 7.5 cm can be painted out of this container?

A)1200
B)234
C)100
D)245

Q42. The volume of a cuboid whose sides are in the ratio of 1:2:4 is same as that of the cube. What is the ratio of the length of diagonal of cuboid to that of cube?

A)3.
B)(1.75)1 / 2
C) 9
D) 3 and 1 / 2

Q43. A cone is inscribed in a hemisphere such that their bases are common. If X is the volume of the cone and Y that of the hemisphere, then what is the value of the Y: X.

A)2:1
B)1:2
C)2:3
D)None of these

Q44. A square has its side equal to the radius of ball. The ball revolves round a side to generate a surface of total area X. If Y be the surface area of the sphere ,then which option is correct?

A) X=Y
B)X=2Y
C)X>Y
D)None of these

Q45. A conical flask of base radius ‘r’ and height ‘h’ is full of water. The water is now poured into a cylinderical flask of radius ‘2r’. What is the height to which water will rise in the flask?

A)h/2
B)h/6
C)h
D)h/12

Q46. The length , breadth and height of a rectangular parallelopiped are in the ratio 6:3:1. If the surface area of a cube is equal to the surface area of this parallelopiped , then what is the ratio of the volume of the cube to the volume to the parallelopiped?

A)1:3
B)3:2
C)3:1
D)none of these

Q47. Find the lateral surface area , if the radius and height of a right circular cone are in the ratio 3:4 and its volume is 96Π cm3?

A)60Πcm2
B) )10Πcm2
C)160Πcm2
D) none of these

Q48. From a cylindrical log whose height is equal to its diameter, the greatest possible sphere has been taken out. What is the fraction of the original log which is cut away?

A)1/2
B)2
C)2/3
D)1/2

Q49. The ratio of the volume of a right cylinder and a right circular cone of the same base and height will be

A)3:1
B)2:3
C)1:1
D)none of these

Q50. The ratio b/w the volume of a sphere and the volume of a circumscribing right cylinder is

A)2:1
B)1:5
C)1:3
D)2:3