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Geometry Questions and Answers

Q1 :

The length of the side of a square whose area is exactly equal to the area of a rectangle whose side are 6.4 m and 2.5 m is

A
  

0.6 m

B
  

2.4 m

C
  

60 m

D
  

4 m

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Q2 :

The outer and inner radii of a metallic spherical shell are 2 cm and 1 cm respectively. If it is melted to make a solid sphere, then the radius of the sphere will be

A
  

7127frac{1}{2} cm

B
  

913 cm 9frac{1}{3} text{ cm }

C
  

713 cm7frac{1}{3} text{ cm}

D
  

3 cm

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Q3 :

A cone of base diameter 20 cm and height 5 cm is melted to form a sphere of radius 5 cm. The volume of the material that remains is

A
  

2 cm32 text{ cm}^3

B
  

5 cm35 text{ cm}^3

C
  

π cm3pi text{ cm}^3

D
  

zero

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Q4 :

A rectangle of sides 10cm and 8 cm is folded to form a cylinder in two different ways. The volume of the bigger cylinder thus formed is

A
  

160πcu cm frac{160}{pi} text{cu cm }

B
  

175πcu cm frac{175}{pi} text{cu cm }

C
  

200πcu cm frac{200}{pi} text{cu cm }

D
  

150πcu cm frac{150}{pi} text{cu cm }

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Q5 :

If the length of a side of rhombus 13 cm and one of its diagonals is of length 24 cm, then the area of rhombus is

A
  

240cm2240 text{cm}^2

B
  

156cm2156 text{cm}^2

C
  

130cm2130 text{cm}^2

D
  

120cm2120 text{cm}^2

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Q6 :

The volume of a right circular cylinder is 1100 cm31100 text{ cm}^3 and the radius of its base is 5cm. The area of its curved surface is

A
  

440 cm2440 text{ cm}^2

B
  

(440+25π) cm2(440 + 25 pi) text{ cm}^2

C
  

(440+50π) cm2(440 + 50pi) text{ cm}^2

D
  

450 cm2450 text{ cm}^2

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Q7 :

A square and an equilateral triangle have equal perimeters. If the area of the equilateral triangle is 163 cm216sqrt3 text{ cm}^2, then the side of the square is 

A
  

4 cm

B
  

42 cm4sqrt2 text{ cm}

C
  

62 cm6sqrt2 text{ cm}

D
  

6 cm

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Q8 :

The height and base radius of a right circular cone are 4 and 3 cm respectively. The total surface area of the cone is 

A
  

15π cm215pi text{ cm}^2

B
  

18π cm218pi text{ cm}^2

C
  

21π cm221pi text{ cm}^2

D
  

24π cm224pi text{ cm}^2

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Q9 :

If both the radius and height of a cone are increased by 50%, then the volume of the cone will increase by

A
  

100%

B
  

200%

C
  

225.50%

D
  

237.50%

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Q10 :

If a solid sphere of radius 34frac{3}{4} m is melted and formed into a right circular cylinder of height 1 m, then the radius of the base of the cylinder will be

A
  

0.75 m

B
  

1.00 m

C
  

1.25 m

D
  

1.50 m

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Q11 :

The radius of the base of a right circular cylinder is halved and the height is increase by 50%. The ratio of the volume of the original cylinder to that of the new cylinder will be

A
  

2 : 3

B
  

8 : 3

C
  

3 : 1

D
  

4 : 1

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Q12 :

The orthocentre of the triangle whose vertices are (0, 0), (3, 0) and (0, 4) is

A
  

(0, 0)

B
  

(0, 2)

C
  

(2, 0)

D
  

(2, 2)

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Q13 :

If ABCD is a rhombus, then 

A
  

AC2+BD2=6AB2text{AC}^2 + text{BD}^2 = 6text{AB}^2

B
  

AC2+BD2=5AB2text{AC}^2 + text{BD}^2 = 5text{AB}^2

C
  

AC2+BD2=4AB2text{AC}^2 + text{BD}^2 = 4text{AB}^2

D
  

AC2+BD2=3AB2text{AC}^2 + text{BD}^2 = 3text{AB}^2

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Q14 :

The circle x2+y2−8x−6y+16=0x^2 + y^2 - 8x - 6y + 16 = 0

A
  

Touches the x-axis

B
  

Touches the y-axis

C
  

Touches both the axes

D
  

Do not Touch any axis

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Q15 :

The area of the circle drawn, with its diameter as the diagonal of the cube of side of length 1 cm each, is

A
  

4π3 sq cmfrac{4pi}{3} text{ sq cm}

B
  

3π2 sq cmfrac{3pi}{2} text{ sq cm}

C
  

3π4 sq cmfrac{3pi}{4} text{ sq cm}

D
  

2π3 sq cmfrac{2pi}{3} text{ sq cm}

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Q16 :

The perimeters of an equilateral triangle and a square are the same. Then

A
  

Area of triangleArea of square=43frac{text{Area of triangle}}{text{Area of square}} = frac{4}{3}

B
  

Area of triangleArea of square=1frac{text{Area of triangle}}{text{Area of square}} = 1

C
  

Area of triangleArea of square=1.5frac{text{Area of triangle}}{text{Area of square}} = 1.5

D
  

Area of triangleArea of square<1frac{text{Area of triangle}}{text{Area of square}} lt 1

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Q17 :

The area of the largest triangle inscribed in a semi-circle of radius R is

A
  

2 R22 text{ R}^2

B
  

R2text{R}^2

C
  

12R2frac{1}{2}text{R}^2

D
  

32R2frac{3}{2}text{R}^2

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Q18 :

A circular disc of area A1text{A}_1 is given. With its radius as the diameter, a circular disc of area A2text{A}_2 is cut out of it. The area of the remaining disc is denoted by A3text{A}_3. Then

A
  

A1A3<16A22text{A}_1 text{A}_3 lt 16 text{A}_2^2

B
  

A1A3>16A22text{A}_1 text{A}_3 gt 16 text{A}_2^2

C
  

A1A3=16A22text{A}_1 text{A}_3 = 16 text{A}_2^2

D
  

A1A3>2A22text{A}_1 text{A}_3 gt 2text{A}_2^2

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Q19 :

If h,ch,c and vv are respectively the height, the curved surface area and volume of a cone, then 3πvh3−c2h2+9v23pi quad vh^3 - c^2h^2 + 9v^2 is equal to

A
  

0

B
  

1

C
  

2

D
  

3

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Q20 :

If the radii of the circular ends of a bucket of height 45 cm are 28 cm and 7 cm respectively, then the capacity of the bucket is

A
  

2310 cm32310 text{ cm}^3

B
  

3080 cm33080 text{ cm}^3

C
  

39270 cm339270 text{ cm}^3

D
  

48510 cm348510 text{ cm}^3

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Q21 :

If the surface area of a cube is 13254 cm2, then the length of its diagonal is:

A
  

443 cm44sqrt3 text{ cm}

B
  

453 cm45sqrt3 text{ cm}

C
  

463 cm46sqrt3 text{ cm}

D
  

473 cm47sqrt3 text{ cm}

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Q22 :

If the radius of a circle is increased such that its circumference increases by 15%, then the area of the circle will increase by:

A
  

31.25%

B
  

32.25%

C
  

33.25%

D
  

34.25%

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Q23 :

If the side of a square is expanded by eight cm, its area expanded by 120 sq cm. The side of the square is:

A
  

2.5 cm

B
  

3.5 cm

C
  

4.5 cm

D
  

5.5 cm

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Q24 :

If a circle touching all n sides of a polygon of perimeter 2p has radius r, then the area of the polygon is:

A
  

(p+n)r(p + n )r

B
  

(2p−n)r(2p - n )r

C
  

prpr

D
  

(p−n)(p - n)

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Q25 :

The number of spherical bullets, each bullet being 4 cm in diameter, that can be made out of a cube of lead whose edge is 44 cm, is:

A
  

2541

B
  

2551

C
  

2561

D
  

2571

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Q26 :

If a square  of area A2frac{text{A}}{2} is cut off from a given square of area A, then the ratio of diagonal of the cut off square to that of the given square is

A
  

1:51:sqrt{5}

B
  

1:51:5

C
  

1:21:sqrt{2}

D
  

1:251:2sqrt{5}

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Q27 :

If the diagonal AC, of a rectangle ABCD is of length 2d and it divides angle BAD in the ratio 1:2, then the area of the rectangle is equal to

A
  

2⋅d2sqrt{2}cdot d^2

B
  

4d24d^2

C
  

22⋅d22sqrt{2}cdot d^2

D
  

3⋅d2sqrt{3} cdot d^2

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Q28 :

If the sides of a triangle are 15 cm, 16 cm and 17 cm, then the area of the triangle is equal to

A
  

162116 sqrt{21} sq cm

B
  

182118 sqrt{21} sq cm

C
  

242124 sqrt{21} sq cm

D
  

302130 sqrt{21} sq cm

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Q29 :

The radius of a wheel is 84 cm. If the wheel makes five revolutions in 5 seconds, then the speed of the wheel, approximately, is

A
  

19 km/h

B
  

33 km/h

C
  

35 km/h

D
  

38 km/h

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Q30 :

If the measurement of each of the interior angles of polygon is 160°160degree, then the number of sides of the polygon would be equal to

A
  

9

B
  

12

C
  

18

D
  

27

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