## Mensuration Part 6: Advance math series 2000 most important questions.

Mensuration Part 6: Advance math series 2000 most important questions.

**Q722. If the radius of a circle is increased by 50%, its area is increased by:**

(a) 125%

(b) 100%

(c) 75%

(d) 50%

**Q723. A bucket contains 2 litres more water when it is filled 80% in comparison when it is filled 662/3****%. What is the capacity of bucket?**

(a) 10 litres

(b) 15 litres

(c) 662/3 litres

(d) 20 litres

**Q724. The diagonal of a right angle isosceles triangle is 5 cm. Its area will be **

(a) 5 sq. cm

(b) 6.25 sq.cm

(c) 6.50 sq.cm

(d) 12.5 sq.cm

**Q725. A well 20 m in diameter is dug 14 m deep and the earth taken out is spread all around it to a width of 5m to form an ambankment. The height of the embankment is:**

(a) 10m

(b) 11m

(c) 11.2m

(d) 11.5m

**Q726**. **The perimeters of two squares are 40 cm and 32 cm. The perimeter of a third square whose area is the difference of the areas of the two squares is**

(a) 24 cm

(b) 42 cm

(c) 40 cm

(d) 20 cm

**Q727**. **The volume of a right circular cylinder, 14 cm in height, is equal to that of a cube whose edge is 11 cm. Taken π = 22/7**** the radius of the base of the cylinder is**

(a) 5.2 cm.

(b) 5.5 cm.

(c) 11.0 cm.

(d) 22.0 cm.

**Q728. A cone is cut at mid point of its height by a frustum parallel to its base. The ratio between the two parts of cone would be**

(a) 1 : 1

(b) 1 : 8

(c) 1 : 4

(d) 1 : 7

**Q729. The length of one side of a rhombus is 6.5 cm and its altitude is 10cm. If the same wire is bent so as to form a circle, then the area enclosed will be: **

(a) 5 cm

(b) 10 cm

(c) 6.5 cm

(d) 26 cm

**Q730. The total surface areas of a cube and a sphere are equal. What will be the ratio between their volumes?**

(a) π : 6

(b) √π : √6

(c) √6 : √π

(d) 6 : π

**Q731. If the volume of a right circular cylinder is 9π****h m ^{3}, where h is its height in metres, then the diameter of the base of the cylinder is equal to**

(a) 3m

(b) 6m

(c) 9m

(d) 12m

**Q732. From a point within an equilateral triangle perpendiculars. Drawn to the three sides, are 6 cm, 7 cm and 8 cm respectively, the length of the side of the triangle is**

(a) 7 cm

(b) 10.5 cm

(c) 14 √3 cm

(d) 14√3/3 cm

**Q733.** **A soap cake is of size 8 cm x 5 cm x 4 cm. ****The number of such soap cakes that can be packed in a box measuring 56 cm x 35 cm x 28 cm is : **

(a) 49

(b) 196

(c) 243

(d) 343

**Q734. A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is:**

(a) 9m

(b) 12m

(c) 18m

(d) 36m

**Q735.** **If the volume and surface area of a sphere are numerically the same, then its radius is:**

(a) 1 unit

(b) 2 units

(c) 3 units

(d) 4 units

**Q736. A hollow iron pipe is 21 cm long and its exterior diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8g/cm ^{3}, then the weight of the pipe is (Taken π = 22/7)**

(a) 3.696 kg

(b) 3.6 kg

(c) 36 kg

(d) 36.9 kg

**Q737. The sides of a triangle are in the ratio 3 : 4 : 5. The measure of the largest angle of the triangle is**

(a) 60^{0}

(b) 90^{0}

(c) 120^{0}

(d) 150^{0}

**Q738.** **If the side of a square is increased by 25%, then its area is increased by 25%, then its area is increased by:**

(a) 25%

(b) 55%

(c) 40.5%

(d) 56.25%

**Q739. The perimeter of a triangle is 30 cm and its area is 30 cm ^{2}. If the largest side measures 13 cm, what is the length of the smallest side of the triangle?**

(a) 3 cm

(b) 4 cm

(c) 5 cm

(d) 6 cm

**Q740. Each side of a regular hexagon is 1 cm. The area of the hexagon is**

(a) 3√3/2 cm^{2}

(b) 3√3/4 cm^{2}

(c) 4√3 cm^{2}

(d) 3√2 cm^{2}

**Q741. Each of the measure of the radius of base of a cone and that of a sphere is 8 cm. Also, the volumes of these two solids are equal. The slant height of the cone is**

(a) 8√17 cm

(b) 4√17 cm

(c) 34√2 cm

(d) 34 cm.

**Q742. If the circumference of a circle is reduced by 50%, its area will be reduced by**

(a) 12.5%

(b) 25%

(c) 50%

(d) 75%

**Q743. The volume of a sphere is **** 88/12 x (14) ^{3 }cm^{3}. The curved surface of the sphere is (Taking p = 22/7)**

(a) 2424 cm^{2}

(b) 2446 cm^{2}

(c) 2484cm^{2}

(d) 2464 cm^{2}

**Q744. The diameters of two hollow spheres made from the same metal sheet are 21 cm and 17.5 cm respectively. The ratio of the areas of metal sheets required for making the two spheres is**** **

(a) 6 : 5

(b) 36 : 25

(c) 3 : 2

(d) 18 : 25

**Q745. A circle is inscribed in a square. An equilateral triangle of side 4√3**** cm is inscribed in that circle. The length of the diagonal of the square in centimeters is**

(a) 4√2

(b) 8

(c) 8√2

(d) 16

**Q746. The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750m ^{2}. The length of the hall is:**

(a) 15m

(b) 22.5m

(c) 25m

(d) 30m

**Q747.** **The area of the largest triangle, that can be inscribed in a semicircle of radius r cm, is**

(a) 2r cm^{2}

(b) r^{2} cm^{2}

(c) 2r^{2} cm^{2}

(d) 1/2 r^{2} cm^{2}

**Q748.** **The diameter of the base of a cylindrical drum is 35 dm., and the height is 24 dm. It is full of kerosene. How many tins each of size 25cm x 22 cm x 35 cm ****can be filled with kerosene from the drum? (use π = 22/7****)**

(a) 1200

(b) 1020

(c) 600

(d) 120

**Q749. A hollow spherical metallic ball has an external diameter 6 cm and is **** 1/2 cm thick. The volume of the ball (in cm ^{3}) is (Taken π =22/7) **

(a) 41 2/3

(b) 37 2/3

(c) 47 2/3

(d) 40 2/3

**Q750.** **If the volumes of two cubes are in the ratio 27: 1,the ratio of their edges is**

(a) 3: 1

(b) 27: 1

(c) 16: 1

(d) 4: 1

**Q751. ** **If the volumes of two cubes are in the ratio 27: 64, then the ratio of their total surface areas is:**

(a) 27: 64

(b) 3: 4

(c) 9: 16

(d) 3: 8

**Q752. ** **The area of the incircle of an equilateral triangle of side 42 cm is (Taken π = 22/7)**

(a) 231 cm^{2}

(b) 462 cm^{2}

(c) 22 √3 cm^{2}

(d) 924 cm^{2}

**Q753. ** **A wooden box measures 20 cm by 12 cm by 10 cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cubic cm) is**

(a) 960

(b) 519

(c) 2400

(d) 1120

**Q754.** **A cuboidal block of 6 cm x 9 cm x 12 cm ****is cut up into exact number of equal cubes. The least possible number of cubes will be**

(a) 6

(b) 9

(c) 24

(d) 30

**Q755.** **The area of a regular hexagon of side 2√3**** cm is:**

(a) 18√3 cm^{2}

(b) 12√3 cm^{2}

(c) 36√3 cm^{2}

(d) 27√3 cm^{2}

**Q756.** **If the radius of the base of a cone be doubled and height is left unchanged. Then ratio of the volume of new cone to that of the original cone will be:**

(a) 1: 4

(b) 2: 1

(c) 1: 2

(d) 4: 1

**Q757.** **The perimeter of a rhombus is 40 cm. If the length of one of its diagonals be 12 cm, the length of the other diagonal is**

(a) 14 cm

(b) 15 cm

(c) 16 cm

(d) 12 cm

**Q758.** **Spheres A and B have their radii 40 cm and 10 cm respectively. Ratio of surface area of A to the surface area of B is:**

(a) 1: 16

(b) 4: 1

(c) 1: 4

(d) 16: 1

**Q759.** **A cistern 6m long and 4 m wide, contains water up to a depth of 1 m 25 cm. The total area of the wet surface is**

(a) 55m^{2}

(b) 53.5m^{2}

(c) 50m^{2}

(d) 49m^{2}

**Q760.** **Three coins of the same size (radius 1 cm) are placed on a table such that each of them touches the other two. The area enclosed by the coins is**** **

(a) (π/2 – √3 )cm^{2 }

(b) (√3 – π/2 )cm^{2}

(c) (2√3 – π/2 )cm^{2}

(d) (3√3 – π/2 )cm^{2}

**Q761. The ratio of bases of two triangles is x: y and that of their areas is a: b. Then the ratio of their corresponding altitudes will be:**

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