CBSE Class 9 Maths Surface Areas and Volumes MCQs Set C

Question. The ratio of the volume and surface area of a sphere of unit radius
(A) 4 : 3
(B) 3 : 4
(C) 1 : 3
(D) 3 : 1

Answer: C

Question. A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
(A) 4
(B) 3
(C) 6
(D) 8

Answer: C

Question. Two identical right circular cones each of height 2 cm are placed as shown in diagram (each is vertical, apex downward). At the start, the upper cone is full of water and lower cone is empty.
Then water drips down through a hole in the apex of upper cone into the lower cone. The height of water in the lower cone at the moment when height of water in upper cone is 1 cm is

Answer: D

Question. A sphere and a cube are of the same height. The ratio of their volume is
(A) 3 : 4
(B) 21 : 11
(C) 4 : 3
(D) 11 : 21

Answer: D

Question. The largest sphere is cut off from a cube of side 5 cm. The volume of the sphere will be
(A) 27 π cm³
(B) 30 π cm³
(C) 108 π cm²
(D) 125 π/6 cm³

Answer: D

Question. Vertical and horizontal cross-sections of a right circular cylinder are always respectively
(A) rectangle, square
(B) rectangle, circle
(C) square, circle
(D) rectangle, ellipse

Answer: B

Question. A right cylindrical vessel is full with water. How many right cones having same diameter and height as of right cylinder will be needed to store that water?
(A) 2
(B) 4
(C) 3
(D) 5

Answer: C

Question. Two cylinders of same volume have their heights in the ration 1 : 3. Then the ratio of their radii is
(A) √3 :1
(B) √2 :1
(C) √5 : 2
(D) 2: v5

Answer: A

Question. ABC is a right angled triangle with ∠ABC = 90º . AH is drawn perpendicular to BC where H lies on BC. If AB = 60 cm and AC = 80 cm, then BH =

(A) 36 cm
(B) 32 cm
(C) 24 cm
(D) 30 cm

Answer: A

Question. The area of a trapezium is 28 cm2 and one of its parallel sides 6 cm. If its altitude is 4 cm., then its other parallel side is
(A) 8 cm
(B) 4 cm
(C) 6 cm
(D) 9 cm

Answer: A

Question. The area of the union of all squares with side 1 cm whose centre lies on a fixed square with side 1 cm euqals
(A) (3+π/4) cm³
(B) (π/2 + 2√2 + 1) cm²
(C) (7/2) cm²
(D) (2√2 + 2)cm²

Answer: B

Question. If the area of a triangle with base x is equal to area of a square of side x, the altitude of the triangle is
(A) x/2
(B) x
(C) √2x
(D) 2x

Answer: A

Question. The ratio of the areas of a square to that of a square drawn on its diagonal is
(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 1 : 4

Answer: B

Question. A man bought a rectangle plot of 144 m length and 64 m width. In exchange for this field he wanted to buy a square field of the same area. Then the side of the square field would be
(A) 104 m
(B) 208 m
(C) 96 m
(D) 406 m

Answer: C

Question. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between surface areas of two solids is
(A) 284 cm²
(B) 286 cm²
(C) 296 cm²
(D) 280 cm²

Answer: B

Question. Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted without any loss of metal into a single cube. The edge of new cube is
(A) 6 cm
(B) 12 cm
(C) 9 cm
(D) 10 cm

Answer: A

Question. If length, breadth and height of rectangular parallelopiped are in ratio 6 : 5 : 4 and total surface area is 33,300 m2, then length breadth and height of parallelopiped are in (m)
(A) 90, 75 , 70
(B) 85, 75, 60
(C) 90, 75, 60
(D) 80, 70, 60

Answer: C

Question. The radius of the cylinder whose lateral surface area is 704 cm23 and height 8 cm, is
(A) 6 cm
(B) 4 cm
(C) 8 cm
(D) 14 cm

Answer: D

Question. A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. The volume of the wood, is
(A) 80,000 cu cm
(B) 82,125 cu cm
(C) 84,000 cu cm
(D) 85,000 cu cm

Answer: B

Question. Four circles of equal radii are centred at the four vertices of a square. These 4 circles touch a fifth circle of equal radius placed inside the square. The ratio of the shaded area of the circles to the unshaded area of the circles is 

(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 2 : 5

Answer: B

Question. The ratio of radii of two cylinders is 1: √3 and heights are in the ratio 2 : 3 The ratio of their volume is
(A) 1 : 9
(B) 2 : 9
(C) 4 : 9
(D) 5 : 9

Answer: B

Question. A solid cube is chopped off at each of its 8 corners to create an equilateral triangle with 3 new corners. The 24 corners are now joined to each other by diagonals. How many of these diagonals completely lie inside the cube?
(A) 120
(B) 108
(C) 96
(D) 100

Answer: A

Question. Two cubes have volume in the ratio 1 : 27. The ratio of the area of the face of one to that of the other is
(A) 1 : 3
(B) 1 : 6
(C) 1 : 9
(D) 1 : 18

Answer: C

Question. The surface areas of the six faces of a rectangular solid are 4, 4, 8, 8, 18 and 18 square centimetres.
The volume of the solid, in cubic centimetres is
(A) 24
(B) 48
(C) 60
(D) 324

Answer: A

Question. Instead of waling along two adjacent sides of rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side, is
(A) 1/2
(B) 2/3
(C) 1/4
(D) 3/4

Answer: D

Question. A rectangle field has its length and breadth in the ratio 5 : 3. Its area is 3.75 hectares. The cost of fencing it at Rs. 5 per meter is
(A) Rs. 400
(B) Rs. 4000
(C) Rs. 1000
(D) Rs. 500

Answer: B

Question. Two rectangles ABCD and DBEF are as shown in the figure. The area of rectangle DBEF in square units is 

(A) 10
(B) 12
(C) 14
(D) 15

Answer: B

Question. The diagonals of a rhombus are 7.5 cm and 12 cm. Then the area of rhombus is
(A) 45 cm²
(B) 90 cm²
(C) 22.5 cm²
(D) 180 cm²

Answer: A

Question. How many diagonals does a 12 - sided regular polygon have?
(A) 35
(B) 50
(C) 54
(D) 30

Answer: C

Question. What change in percent is made in the area of a rectangle by decreasing its length and increasing its breadth by 5%?
(A) 2.5% increase
(B) 0.25 % increase
(C) 0.25% decrease
(D) 2.5 % decrease

Answer: B

Question. The ratio of areas of two squares, one having double its diagonal than the other is
(A) 3 : 2
(B) 4 : 1
(C) 3 : 1
(D) 4 : 3

Answer: C

Question. A child walked 5 m to cross a rectangular field diagonally. If breadth of field is 3 m, its length is
(A) 4 m
(B) 3 m
(C) 10 m
(D) 6 m

Answer: A

Question. The length of longest rod that can fit in a cubical room of 4 m side is
(A) 8.66 m
(B) 5.196 m
(C) 6.928 m
(D) 5 m

Answer: C

Question. The area of a rhombus is 28 cm² and one of its diagonals is 4 cm. Its perimeter is
(A) 4 √53 m
(B) 36 cm
(B) 2 √53 m
(D) None of these

Answer: A

Question. The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of these sides is 13 cm. Its area is
(A) 72 cm²
(B) 12 35 cm²
(C) 24 35 cm²
(D) 150 cm²

Answer: B

Question. The number of surfaces in right circular cylinder, is
(A) 1
(B) 2
(C) 3
(D) 4

Answer: C

Question. A square pond has 2 m sides and is 1 m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, the what would be the volume of earth to be removed ? 

(A) (2π – 4) m³
(B) (4π – 4) m³
(C) (4π – 2) m³
(D) (2π – 2) m³

Answer: A

Question. Two circular cylinders of equal volume have heights in the ratio of 1 “ 2. The ratio of their radii is
(A) 1 : 2
(B) 2 : 1
(C) 1: √2
(D) √2 :1

Answer: D

Question. A rectangle ground is 90 m long and 32 m broad. In the middle of the ground there is a circular tank of radius 14 meters. The cost of turfing the remaining portion at the rate of Rs. 2.50 per square meter is
(A) Rs. 6000
(B) Rs. 5660
(C) Rs. 5800
(D) Rs. 5750

Answer: B

Question. If the diagonal of a square is doubled, the area of the square becomes
(A) 2 times
(B) 3 times
(C) 4 times
(D) 6 times

Answer: C

Question. The area of the field if M is the mid point of LN is 

(A) 15200 sq. units
(B) 13300 sq. units
(C) 15000 sq. units
(D) 27800 sq. units

Answer: B

Question. The area of the trapezium ABCD as shown in the figure (in square units) is 

(A) 222
(B) 111
(C) 224
(D) 116

Answer: A

Question. What is the length of AC? (All dimensions are in cm) 

(A) 95
(B) 75
(C) 85
(D) 65

Answer: D

Question. What is the volume of the rectangular solid shown below ? 

(A) 520 cm³
(B) 725 cm³
(C) 420 cm³
(D) 720 cm³

Answer: D

Question. The hypotenuse of a triangle is 29 cm and one of its sides is 20 cm, then the other side is
(A) 20 cm
(B) 21 cm
(C) 27 cm
(D) 25 cm

Answer: B

Question. A hoop is resting vertically at stair case as shown in the diagram. AB = 12 cm and BC = 8 cm. The radius of the hoop is 

(A) 13 cm
(B) 12 √2 cm
(C) 14 cm
(D) 13 √2 cm

Answer: A

Question. O is the centre of the regular pentagon. What part of the whole pentagon is the shaded region ?

(A) 10 %
(B) 20 %
(C) 25 %
(D) 30 %

Answer: D

Question. The perimeter of the figure given below correct to one decimal place is 

(A) 56.0 m
(B) 56.6 m
(C) 57.2 m
(D) 57.9 m

Answer: B

Question. The ratio between the length and the perimeter of a rectangular plot is 1 : 3 and the ratio between the breadth and perimeter of that plot is 1 : 6. What is the ratio between the length and area of that plot ?
(A) 2 : 1
(B) 1 : 6
(C) 1 : 8
(D) Data inadequate

Answer: D

Question. A cylindrical tower is 5 m in diameter and 14 meter high. The cost of white washing its curved surface at 50 paisa per m2 is
(A) Rs. 90
(B) Rs. 97
(C) Rs. 110
(D) Rs. 95

Answer: C